#### Sample records for fractional order systems

1. DYNAMICS OF FRACTIONAL ORDER CHAOTIC SYSTEM

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M. Jana

2017-02-01

Full Text Available This paper deals with the dynamics of chaos and synchronization for fractional order chaotic system. For fractional order derivative Captuo definition is used here and numerical simulations are done using Predictor-Correctors scheme by Diethlm based on the Adams-Baseforth-Moulton algorithm. Stability analysis is discussed here for non linear fractional order chaotic system and synchronization is achieved between two non identical fractional order chaotic systems: Finance chaotic system(driving systemand Lorenz system(response systemvia active control.Numerical simulations are performed to show the effectiveness of these approaches.

2. Control of Initialized Fractional-Order Systems

Science.gov (United States)

Hartly, Tom T.; Lorenzo, Carl F.

2002-01-01

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

3. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

KAUST Repository

N'Doye, Ibrahima

2015-07-01

This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

4. Stability analysis of distributed order fractional chen system.

Science.gov (United States)

Aminikhah, H; Refahi Sheikhani, A; Rezazadeh, H

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.

5. Stability Analysis of Distributed Order Fractional Chen System

Science.gov (United States)

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

6. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

KAUST Repository

N U+02BC Doye, Ibrahima

2018-02-13

In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

7. State space realization of fractional order systems

International Nuclear Information System (INIS)

Djamah, T.; Mansouri, R.; Djennoune, S.; Bettayeb, M.

2009-01-01

In the past few years, fractional calculus appeared to be a useful tool for the modeling and control of dynamic systems. Although, some methods of the control theory have been developed for the commensurate case, the difficulties of the non commensurate called generalized fractional systems still remain unsolved. In this paper, a method is presented for obtaining the state space model of a generalized fractional system starting from its transfer function. The method remains valid for the particular cases of commensurate and integer systems. An application to some examples illustrates the algorithm.

8. Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation

CERN Document Server

Petráš, Ivo

2011-01-01

"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...

9. Fractional order control and synchronization of chaotic systems

CERN Document Server

2017-01-01

The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional contro...

10. The adaptive synchronization of fractional-order Liu chaotic system ...

fractional-order chaotic systems, investigating the stabilization conditions by using the projective method. In [13], a simple but efficient way to control the fractional-order chaos system, using the TS fuzzy model and adaptive regulation mechanism was presented. In. [14], the second-order sliding mode control to stabilize one ...

11. Intelligent Fractional Order Systems and Control An Introduction

CERN Document Server

Pan, Indranil

2013-01-01

Fractional order calculus is finding increasing interest in the control system community. Hardware realizations of fractional order controllers have sparked off a renewed zeal into the investigations of control system design in the light of fractional calculus. As such many notions of integer order LTI systems are being modified and extended to incorporate these new concepts. Computational Intelligence (CI) techniques have been applied to engineering problems to find solutions to many hitherto intractable conundrums and is a useful tool for dealing with problems of higher computational complexity. This book borders on the interface between CI techniques and fractional calculus, and looks at ways in which fractional order control systems may be designed or enhanced using CI based paradigms. To the best of the author’s knowledge this is the first book of its kind exclusively dedicated to the application of computational intelligence techniques in fractional order systems and control. The book tries to assimil...

12. Active disturbance rejection control for fractional-order system.

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Li, Mingda; Li, Donghai; Wang, Jing; Zhao, Chunzhe

2013-05-01

Fractional-order proportional-integral (PI) and proportional-integral-derivative (PID) controllers are the most commonly used controllers in fractional-order systems. However, this paper proposes a simple integer-order control scheme for fractional-order system based on active disturbance rejection method. By treating the fractional-order dynamics as a common disturbance and actively rejecting it, active disturbance rejection control (ADRC) can achieve the desired response. External disturbance, sensor noise, and parameter disturbance are also estimated using extended state observer. The ADRC stability of rational-order model is analyzed. Simulation results on three typical fractional-order systems are provided to demonstrate the effectiveness of the proposed method. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

13. The synchronisation of fractional-order hyperchaos compound system

This paper presents a new compound synchronisation scheme among four hyperchaotic memristor system with incommensurate fractional-order derivatives. First a new controller was designed based on adaptivetechnique to minimise the errors and guarantee compound synchronisation of four fractional-order memristor ...

14. Dynamics of fractional-ordered Chen system with delay

In the present paper the effect of delay on chaos in fractional-order Chen system is investigated. It is observed that ... There has been an explosion of activity in dynamical systems theory in the past two decades. Most activity is ... open new possibilities since the evolution depends on entire history. Fractional differential ...

15. Identification of fractional order systems using modulating functions method

KAUST Repository

Liu, Dayan

2013-06-01

The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

16. Genetic Algorithm-Based Identification of Fractional-Order Systems

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Shengxi Zhou

2013-05-01

Full Text Available Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA is proposed in this paper. The multi-variable parameter identification is converted into a parameter optimization by applying GA to the identification of fractional-order systems. To evaluate the identification accuracy and stability, the time-domain output error considering the condition variation is designed as the fitness function for parameter optimization. The identification process is established under various noise levels and excitation levels. The effects of external excitation and the noise level on the identification accuracy are analyzed in detail. The simulation results show that the proposed method could identify the parameters of both commensurate rate and non-commensurate rate fractional-order systems from the data with noise. It is also observed that excitation signal is an important factor influencing the identification accuracy of fractional-order systems.

17. Chaos synchronization of the fractional-order Chen's system

International Nuclear Information System (INIS)

Zhu Hao; Zhou Shangbo; He Zhongshi

2009-01-01

In this paper, based on the stability theorem of linear fractional systems, a necessary condition is given to check the chaos synchronization of fractional systems with incommensurate order. Chaos synchronization is studied by utilizing the Pecora-Carroll (PC) method and the coupling method. The necessary condition can also be used as a tool to confirm results of a numerical simulation. Numerical simulation results show the effectiveness of the necessary condition.

18. Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

International Nuclear Information System (INIS)

Jia Li-Xin; Dai Hao; Hui Meng

2010-01-01

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method

19. The Active Fractional Order Control for Maglev Suspension System

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Peichang Yu

2015-01-01

Full Text Available Maglev suspension system is the core part of maglev train. In the practical application, the load uncertainties, inherent nonlinearity, and misalignment between sensors and actuators are the main issues that should be solved carefully. In order to design a suitable controller, the attention is paid to the fractional order controller. Firstly, the mathematical model of a single electromagnetic suspension unit is derived. Then, considering the limitation of the traditional PD controller adaptation, the fractional order controller is developed to obtain more excellent suspension specifications and robust performance. In reality, the nonlinearity affects the structure and the precision of the model after linearization, which will degrade the dynamic performance. So, a fractional order controller is addressed to eliminate the disturbance by adjusting the parameters which are added by the fractional order controller. Furthermore, the controller based on LQR is employed to compare with the fractional order controller. Finally, the performance of them is discussed by simulation. The results illustrated the validity of the fractional order controller.

20. Chaos in a fractional-order Roessler system

International Nuclear Information System (INIS)

Zhang Weiwei; Zhou Shangbo; Li Hua; Zhu Hao

2009-01-01

The dynamic behaviors in the fractional-order Roessler equations were numerically studied. Basic properties of the system have been analyzed by means of Lyapunov exponents and bifurcation diagrams. The parameter and the derivative order ranges used were relatively broad. Regular motions (including period-3 motion) and chaotic motions were examined. The chaotic motion identified was validated by the positive Lyapunov exponent.

1. The synchronisation of fractional-order hyperchaos compound system

Science.gov (United States)

Noghredani, Naeimadeen; Riahi, Aminreza; Pariz, Naser; Karimpour, Ali

2018-02-01

This paper presents a new compound synchronisation scheme among four hyperchaotic memristor system with incommensurate fractional-order derivatives. First a new controller was designed based on adaptive technique to minimise the errors and guarantee compound synchronisation of four fractional-order memristor chaotic systems. According to the suitability of compound synchronisation as a reliable solution for secure communication, we then examined the application of the proposed adaptive compound synchronisation scheme in the presence of noise for secure communication. In addition, the unpredictability and complexity of the drive systems enhance the security of secure communication. The corresponding theoretical analysis and results of simulation validated the effectiveness of the proposed synchronisation scheme using MATLAB.

2. The adaptive synchronization of fractional-order Liu chaotic system ...

In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule ...

3. Inverse synchronization of coupled fractional-order systems through ...

calculus (integration and differentiation of fractional order) can go back to Liouville,. Riemann, Leibniz, Grunwald, and Letnikovis [1–3]. Nowadays, this branch of mathe- matics has found applications in a number of different areas ranging from physics to engineering. It is known that many systems in interdisciplinary fields ...

4. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

KAUST Repository

Belkhatir, Zehor

2017-05-31

This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

5. Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders

DEFF Research Database (Denmark)

Nielsen, Morten Ørregaard

2009-01-01

In this paper a nonparametric variance ratio testing approach is proposed for determining the number of cointegrating relations in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating....... The asymptotic distribution theory for the proposed test is non-standard but easily tabulated. Monte Carlo simulations demonstrate excellent finite sample properties, even rivaling those of well-specified parametric tests. The proposed methodology is applied to the term structure of interest rates, where...

6. Inverse synchronization of coupled fractional-order systems through ...

A general explicit coupling via an open-plus-closed-loop control for inverse synchronization of two .... derivative [51], which is in essence an improved version of Adams–Bashforth–Moulton algorithm. The following is a ... OPCL control has found its applications in the synchronization of both integer-order and fractional-order ...

7. Frequency domain analysis and applications for fractional-order control systems

International Nuclear Information System (INIS)

Wang Jifeng; Li Yuankai

2005-01-01

This paper is concerned with the frequency domain analysis for fractional-order control systems. By Bode diagrams and Nyquist contour, the relationship of frequency properties between fractional-order systems and integer-order ones is found. A method of judging fractional-order system transfer functions from their frequency properties is provided

8. Fractional-order devices

CERN Document Server

Biswas, Karabi; Caponetto, Riccardo; Mendes Lopes, António; Tenreiro Machado, José António

2017-01-01

This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator...

9. Numerical solutions of the nonlinear fractional-order brusselator system by Bernstein polynomials.

Science.gov (United States)

Khan, Hasib; Jafari, Hossein; Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

2014-01-01

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.

10. A Model of Gear Transmission: Fractional Order System Dynamics

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Katica (Stevanović Hedrih

2010-01-01

Full Text Available A theoretical model of multistep gear transmission dynamics is presented. This model is based on the assumption that the connection between the teeth of the gears is with properties within the range from ideal clasic to viscoelastic so that a new model of connection between the teeth was expressed by means of derivative of fractional order. For this model a two-step gear transmision with three degrees of freedom of motion has been used. The obtained solutions are in the analytic form of the expansion according to time. As boundary cases this model gives results for the case of ideally elastic connection of the gear teeth and for the case of viscoelastic connection of the gear teeth, as well. Eigen fractional modes are obtained and a vizualization is done.

11. Fractional Order Generalized Information

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2014-04-01

Full Text Available This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

12. Nonlinear dynamics and chaos in a fractional-order financial system

International Nuclear Information System (INIS)

Chen Weiching

2008-01-01

This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found

13. Nonlinear dynamics and chaos in a fractional-order financial system

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Chen Weiching [Department of Information Management, Yuanpei University, Hsinchu, Taiwan (China)], E-mail: wcc137@mail.yust.edu.tw

2008-06-15

This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found.

14. Fractional order differentiation by integration: An application to fractional linear systems

KAUST Repository

Liu, Dayan

2013-02-04

In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.

15. Joint estimation of the fractional differentiation orders and the unknown input for linear fractional non-commensurate system

KAUST Repository

Belkhatir, Zehor

2015-11-05

This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.

16. Parametric Control on Fractional-Order Response for Lü Chaotic System

KAUST Repository

2013-04-10

This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.

17. Dynamics of fractional-ordered Chen system with delay

Fractional calculus is a branch of Mathematics which deals with differentiation and inte- gration of arbitrary ... of fractional calculus to various branches of science and engineering have been real- ized only recently. ... in later works from the viewpoints of theoretical understanding as well as applications such as secure ...

18. Synchronization and an application of a novel fractional order King Cobra chaotic system

Energy Technology Data Exchange (ETDEWEB)

Muthukumar, P., E-mail: muthukumardgl@gmail.com; Balasubramaniam, P., E-mail: balugru@gmail.com [Department of Mathematics, Gandhigram Rural Institute‐Deemed University, Gandhigram 624 302, Tamilnadu (India); Ratnavelu, K., E-mail: kuru052001@gmail.com [Faculty of Science, Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)

2014-09-01

In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.

19. Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations

Directory of Open Access Journals (Sweden)

2010-01-01

Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.

20. Hurwitz stability analysis of fractional order LTI systems according to principal characteristic equations.

Science.gov (United States)

Alagoz, Baris Baykant

2017-09-01

With power mapping (conformal mapping), stability analyses of fractional order linear time invariant (LTI) systems are carried out by consideration of the root locus of expanded degree integer order polynomials in the principal Riemann sheet. However, it is essential to show the left half plane (LHP) stability analysis of fractional order characteristic polynomials in the s plane in order to close the gap emerging in stability analyses of fractional order and integer order systems. In this study, after briefly discussing the relation between the characteristic root orientations and the system stability, the author presents a methodology to establish principal characteristic polynomials to perform the LHP stability analysis of fractional order systems. The principal characteristic polynomials are formed by factorizing principal characteristic roots. Then, the LHP stability analysis of fractional order systems can be carried out by using the root equivalency of fractional order principal characteristic polynomials. Illustrative examples are presented to explain how to find equivalent roots of fractional order principal characteristic polynomials in order to carry out the LHP stability analyses of fractional order nominal and interval systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

1. Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control

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Jianeng Tang

2014-01-01

Full Text Available Chaos synchronization of different fractional order time-delay chaotic systems is considered. Based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method. At last, effects of the fraction order and the time delay on synchronization are further researched.

2. Robust control for fractional variable-order chaotic systems with non-singular kernel

Science.gov (United States)

Zuñiga-Aguilar, C. J.; Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Romero-Ugalde, H. M.

2018-01-01

This paper investigates the chaos control for a class of variable-order fractional chaotic systems using robust control strategy. The variable-order fractional models of the non-autonomous biological system, the King Cobra chaotic system, the Halvorsen's attractor and the Burke-Shaw system, have been derived using the fractional-order derivative with Mittag-Leffler in the Liouville-Caputo sense. The fractional differential equations and the control law were solved using the Adams-Bashforth-Moulton algorithm. To test the control stability efficiency, different statistical indicators were introduced. Finally, simulation results demonstrate the effectiveness of the proposed robust control.

3. Stabilization of generalized fractional order chaotic systems using state feedback control

International Nuclear Information System (INIS)

2004-01-01

In this paper, we address the problem of chaos control of three types of fractional order systems using simple state feedback gains. Electronic chaotic oscillators, mechanical 'jerk' systems, and the Chen system are investigated when they assume generalized fractional orders. We design the static gains to place the eigenvalues of the system Jacobian matrices in a stable region whose boundaries are determined by the orders of the fractional derivatives. We numerically demonstrate the effectiveness of the controller in eliminating the chaotic behavior from the state trajectories, and driving the states to the nearest equilibrium point in the basin of attraction. For the recently introduced Chen system, in particular, we demonstrate that with a proper choice of model parameters, chaotic behavior is preserved when the system order becomes fractional. Both state and output feedback controllers are then designed to stabilize a generalized fractional order Chen system

4. The fractional-order modeling and synchronization of electrically coupled neuron systems

KAUST Repository

2012-11-01

In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.

5. Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems

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Jian Yuan

2015-01-01

Full Text Available This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems. We firstly introduce a fractional integral sliding manifold for the nominal systems. Secondly we prove the stability of the corresponding fractional sliding dynamics. Then, by introducing a Lyapunov candidate function and using the Mittag-Leffler stability theory we derive the desired sliding control law. Furthermore, we prove that the proposed sliding manifold is also adapted for the fractional systems in the presence of uncertainties and external disturbances. At last, we design a fractional adaptation law for the perturbed fractional systems. To verify the viability and efficiency of the proposed fractional controllers, numerical simulations of fractional Lorenz’s system and Chen’s system are presented.

6. IMC-PID-fractional-order-filter controllers design for integer order systems.

Science.gov (United States)

Maâmar, Bettayeb; Rachid, Mansouri

2014-09-01

One of the reasons of the great success of standard PID controllers is the presence of simple tuning rules, of the automatic tuning feature and of tables that simplify significantly their design. For the fractional order case, some tuning rules have been proposed in the literature. However, they are not general because they are valid only for some model cases. In this paper, a new approach is investigated. The fractional property is not especially imposed by the controller structure but by the closed loop reference model. The resulting controller is fractional but it has a very interesting structure for its implementation. Indeed, the controller can be decomposed into two transfer functions: an integer transfer function which is generally an integer PID controller and a simple fractional filter. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

7. Identification of fractional-order systems with unknown initial values and structure

Energy Technology Data Exchange (ETDEWEB)

Du, Wei, E-mail: duwei0203@gmail.com [Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237 (China); Miao, Qingying, E-mail: qymiao@sjtu.edu.cn [School of Continuing Education, Shanghai Jiao Tong University, Shanghai 200030 (China); Tong, Le, E-mail: tongle0328@gmail.com [Faculty of Applied Science and Textiles, The Hong Kong Polytechnic University, Hong Kong (China); Tang, Yang [Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237 (China)

2017-06-21

In this paper, the identification problem of fractional-order chaotic systems is proposed and investigated via an evolutionary optimization approach. Different with other studies to date, this research focuses on the identification of fractional-order chaotic systems with not only unknown orders and parameters, but also unknown initial values and structure. A group of fractional-order chaotic systems, i.e., Lorenz, Lü, Chen, Rössler, Arneodo and Volta chaotic systems, are set as the system candidate pool. The identification problem of fractional-order chaotic systems in this research belongs to mixed integer nonlinear optimization in essence. A powerful evolutionary algorithm called composite differential evolution (CoDE) is introduced for the identification problem presented in this paper. Extensive experiments are carried out to show that the fractional-order chaotic systems with unknown initial values and structure can be successfully identified by means of CoDE. - Highlights: • Unknown initial values and structure are introduced in the identification of fractional-order chaotic systems; • Only a series of output is utilized in the identification of fractional-order chaotic systems; • CoDE is used for the identification problem and the results are satisfactory when compared with other DE variants.

8. Control and switching synchronization of fractional order chaotic systems using active control technique

KAUST Repository

2013-03-13

This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.

9. The adaptive synchronization of fractional-order Liu chaotic system ...

−a; 02.30.Yy. 1. Introduction. The chaotic behaviour of the dynamic systems can be observed in several real applications in the world, such as circuits, mathematics, power systems, medicine, electrochemical biology, etc. [1,2]. Thus, chaos is ...

10. The synchronisation of fractional-order hyperchaos compound system

2018-01-24

Jan 24, 2018 ... ematics [6], power systems [7,8] etc. The extremely complex non-linear structures of these systems provide them unique features such as extreme sensitivity to ini- tial conditions and continuous frequency spectrum, and allows them to be locally bounded yet globally unstable. [9]. Consequently, chaos theory ...

11. QS synchronization of the fractional-order unified system

State Key Laboratory of Power Transmission Equipment & System Security and New Technology, School of Automation, Chongqing University, Chongqing 400044, People's Republic of China; School of Mathematics, Anhui University, Hefei 230039, People's Republic of China; School of Automation, Beijing Institute of ...

12. The synchronisation of fractional-order hyperchaos compound system

Corresponding author. E-mail: n-pariz@um.ac.ir. MS received 18 October 2016; revised 26 August 2017; accepted 26 September 2017; published online 24 January 2018. Abstract. This paper presents a new compound synchronisation scheme among four hyperchaotic memristor system with incommensurate ...

13. Universal block diagram based modeling and simulation schemes for fractional-order control systems.

Science.gov (United States)

Bai, Lu; Xue, Dingyü

2017-05-08

Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

14. A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos

Directory of Open Access Journals (Sweden)

Shiyun Shen

2017-01-01

Full Text Available One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme.

15. Main chains and eigen modes of fractional order hybrid multipendulum system dynamics

Energy Technology Data Exchange (ETDEWEB)

Hedrih, Katica R. [Faculty of Mechanical Engineering University of Nis, Mathematical Institute SANU, ul. Vojvode Tankosic 3/V/22, 18000- Nis (Serbia)], E-mail: katica@masfak.ni.ac.yu, E-mail: khedrih@eunet.yu

2009-10-15

A short review of the author's research results in the area of the dynamics of pendulum hybrid systems, as well as an analytical approach to the discrete material particle system dynamics containing creep elements with the constitutive stress-strain relation described by the fractional order derivative are presented. The first results presented in this paper are analytical expressions of the modes of three pendulum fractional order system vibrations. It is shown that two time modes (partial solutions) are pure periodical, and four time modes (particular solutions) are 'creeping modes' as a result of the creeping properties influencing standard light elements to the periodical pendulum mode vibrations with corresponding frequencies. By using an analytical approach, for a fractional order hybrid multipendulum system dynamics, eigen main chains, eigen modes and main coordinates are obtained. The second and generalized result concerns the fractional order hybrid multipendulum system dynamics.

16. Main chains and eigen modes of fractional order hybrid multipendulum system dynamics

International Nuclear Information System (INIS)

Hedrih, Katica R.

2009-01-01

A short review of the author's research results in the area of the dynamics of pendulum hybrid systems, as well as an analytical approach to the discrete material particle system dynamics containing creep elements with the constitutive stress-strain relation described by the fractional order derivative are presented. The first results presented in this paper are analytical expressions of the modes of three pendulum fractional order system vibrations. It is shown that two time modes (partial solutions) are pure periodical, and four time modes (particular solutions) are 'creeping modes' as a result of the creeping properties influencing standard light elements to the periodical pendulum mode vibrations with corresponding frequencies. By using an analytical approach, for a fractional order hybrid multipendulum system dynamics, eigen main chains, eigen modes and main coordinates are obtained. The second and generalized result concerns the fractional order hybrid multipendulum system dynamics.

17. Generation and control of multi-scroll chaotic attractors in fractional order systems

International Nuclear Information System (INIS)

2005-01-01

The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations

18. The response analysis of fractional-order stochastic system via generalized cell mapping method

Science.gov (United States)

Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei

2018-01-01

This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

19. State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation

Directory of Open Access Journals (Sweden)

Junhai Luo

2014-01-01

Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.

20. DFIG Based Wind Turbines Behavior Improvement during Wind Variations using Fractional Order Control Systems

Directory of Open Access Journals (Sweden)

2014-12-01

Full Text Available This paper is concerned with behavior analysis and improvement of wind turbines with Doubly Fed Induction Generator (DFIG when using a new fractional-order control strategy during wind variations. A doubly fed induction generator, two types of variable frequency power electronic converters and two input wind waveforms are considered. A fractional-order control strategy is proposed for the wind turbine control unit. Output parameters of the wind turbine are drawn by simulations using MATLAB/Simulink for both fractional-order and integer-order (classic control systems and a complete comparison between these two strategies has been presented. Results show a better operation when using fractional-order control system.

1. Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system

KAUST Repository

N’Doye, Ibrahima

2015-05-23

This paper presents the ℋ∞ static output feedback control of nonlinear fractional-order systems. Based on the extended bounded real lemma, the ℋ∞ control is formulated and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order α belongs to 0 < α < 1. The control approach is finally applied to the regulation of the glucose level in diabetes type 1 treatment. Therefore, it is attempted to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of the system in the presence of meal disturbance. Numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart in the presence of exogenous glucose infusion or meal disturbance. © 2015 Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg

2. Parameter estimation of fractional-order chaotic systems by using quantum parallel particle swarm optimization algorithm.

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Yu Huang

Full Text Available Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.

3. Model-order reduction of lumped parameter systems via fractional calculus

Science.gov (United States)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

4. The Onset of Chaos via Asymptotically Period-Doubling Cascade in Fractional Order Lorenz System

Science.gov (United States)

Lin, Xiaofang; Liao, Binghui; Zeng, Caibin

2017-12-01

Little seems to be known about the chaotification problem in the framework of fractional order nonlinear systems. Based on the negative damping instability mechanism and fractional calculus technique, this paper reports the onset of chaos in fractional order Lorenz system with periodic system parameters via asymptotically period-doubling cascade. To further understand the complex dynamics of the system, some basic properties such as the largest Lyapunov exponents, bifurcation diagram, routes to chaos, asymptotically periodic windows, possible chaotic and asymptotically periodic window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations. Of particular interest is a striking finding that fractional derivative can chaotify the globally stable periodic system without feedback control.

5. Parametric study of the fractional-order Chen-Lee system

Energy Technology Data Exchange (ETDEWEB)

Tam, L.M. [Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Av. Padre Tomas Pereira S.J., Taipa, Macau (China)], E-mail: fstlmt@umac.mo; Tou, W.M.S. [Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Av. Padre Tomas Pereira S.J., Taipa, Macau (China)

2008-08-15

The dynamics of fractional-order systems have attracted a great deal of attention in recent years. In this paper, the effects of parameter changes on the dynamics of the fractional-order Chen-Lee system were studied numerically. The parameter ranges used were relatively broad. The order used for the system was fixed at 2.7 (q{sub 1} = q{sub 2} = q{sub 3} = 0.9). The system displays rich dynamic behaviors, such as a fixed point, periodic motion (including period-3 motion), chaotic motion, and transient chaos. The chaotic motion identified was validated by the confirmation of a positive Lyapunov exponent. Period-doubling routes to chaos in the fractional-order Chen-Lee system were also found.

6. Identification of fractional-order systems with time delays using block pulse functions

Science.gov (United States)

Tang, Yinggan; Li, Ning; Liu, Minmin; Lu, Yao; Wang, Weiwei

2017-07-01

In this paper, a novel method based on block pulse functions is proposed to identify continuous-time fractional-order systems with time delays. First, the operational matrices of block pulse functions for fractional integral operator and time delay operator are derived. Then, these operational matrices are applied to convert the continuous-time fractional-order systems with time delays to an algebraic equation. Finally, the system's parameters along with the differentiation orders and the time delays are all simultaneously estimated through minimizing a quadric error function. The proposed method reduces the computation complexity of the identification process, and also it does not require the system's differentiation orders to be commensurate. The effectiveness of the proposed method are demonstrated by several numerical examples.

7. Synchronization of variable-order fractional financial system via active control method

Science.gov (United States)

Xu, Yufeng; He, Zhimin

2013-06-01

In this paper, we study the chaotic dynamics of a Variable-Order Fractional Financial System (VOFFS). The Variable-Order Fractional Derivative (VOFD) is defined in Caputo type. A necessary condition for occurrence of chaos in VOFFS is obtained. Numerical experiments on the dynamics of the VOFFS with various conditions are given. Based on them, it is shown that the VOFFS has complex dynamical behavior, and the occurrence of chaos depends on the choice of order function. Furthermore, the chaos synchronization of the VOFFS is studied via active control method. Numerical simulations demonstrate that the active control method is effective and simple for synchronizing the VOFFSs with commensurate or incommensurate order functions.

8. Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

Science.gov (United States)

2017-12-01

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of 2.15. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

9. Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations

Directory of Open Access Journals (Sweden)

C. Ünlü

2013-01-01

Full Text Available A modification of the variational iteration method (VIM for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.

10. Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance

Science.gov (United States)

Ding, Da-Wei; Liu, Fang-Fang; Chen, Hui; Wang, Nian; Liang, Dong

2017-12-01

In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractional-order system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the non-commensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally, numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time. Supported by the National Nature Science Foundation of China under Grant No. 61201227, Funding of China Scholarship Council, the Natural Science Foundation of Anhui Province under Grant No. 1208085M F93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B

11. Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

Directory of Open Access Journals (Sweden)

Bin Wang

2016-01-01

Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

12. Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

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Abir Lassoued

2017-01-01

Full Text Available A novel hyperchaotic system with fractional-order (FO terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

13. Stabilization and control of fractional order systems a sliding mode approach

CERN Document Server

2015-01-01

In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis.This monograph is based on the authors' work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashi

14. Robust stability of a class of uncertain fractional order linear systems with pure delay

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Busłowicz Mikołaj

2015-06-01

Full Text Available The paper considers the robust stability problem of uncertain continuous-time fractional order linear systems with pure delay in the following two cases: a the state matrix is a linear convex combination of two known constant matrices, b the state matrix is an interval matrix. It is shown that the system is robustly stable if and only if all the eigenvalues of the state matrix multiplied by delay in power equal to fractional order are located in the open stability region in the complex plane. Parametric description of boundary of this region is derived. In the case a the necessary and sufficient computational condition for robust stability is established. This condition is given in terms of eigenvalue-loci of the state matrix, fractional order and time delay. In the case b the method for determining the rectangle with sides parallel to the axes of the complex plane in which all the eigenvalues of interval matrix are located is given and the sufficient condition for robust stability is proposed. This condition is satisfied if the rectangle multiplied by delay in power equal to fractional order lie in the stability region. The considerations are illustrated by numerical examples.

15. Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

KAUST Repository

Belkhatir, Zehor

2017-06-28

This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise input is decoupled into two algebraic systems of equations. The first system is nonlinear and solves for the time locations iteratively, whereas the second system is linear and solves for the input’s amplitudes. Second, closed form formulas for both the time location and the amplitude are provided in the particular case of single point input. Finally, numerical examples are given to illustrate the performance of the proposed technique in both noise-free and noisy cases. The joint estimation of pointwise input and fractional differentiation orders is also presented. Furthermore, a discussion on the performance of the proposed algorithm is provided.

16. Identification of fractional-order systems via a switching differential evolution subject to noise perturbations

International Nuclear Information System (INIS)

Zhu, Wu; Fang, Jian-an; Tang, Yang; Zhang, Wenbing; Xu, Yulong

2012-01-01

In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.

17. Multiobjective Optimization Design of a Fractional Order PID Controller for a Gun Control System

OpenAIRE

Qiang Gao; Jilin Chen; Li Wang; Shiqing Xu; Yuanlong Hou

2013-01-01

Motion control of gun barrels is an ongoing topic for the development of gun control equipments possessing excellent performances. In this paper, a typical fractional order PID control strategy is employed for the gun control system. To obtain optimal parameters of the controller, a multiobjective optimization scheme is developed from the loop-shaping perspective. To solve the specified nonlinear optimization problem, a novel Pareto optimal solution based multiobjective differential evolution...

18. Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

Directory of Open Access Journals (Sweden)

Hai Zhang

2014-01-01

Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

19. High-order sliding mode observer for fractional commensurate linear systems with unknown input

KAUST Repository

Belkhatir, Zehor

2017-05-20

In this paper, a high-order sliding mode observer (HOSMO) is proposed for the joint estimation of the pseudo-state and the unknown input of fractional commensurate linear systems with single unknown input and a single output. The convergence of the proposed observer is proved using a Lyapunov-based approach. In addition, an enhanced variant of the proposed fractional-HOSMO is introduced to avoid the peaking phenomenon and thus to improve the estimation results in the transient phase. Simulation results are provided to illustrate the performance of the proposed fractional observer in both noise-free and noisy cases. The effect of the observer’s gains on the estimated pseudo-state and unknown input is also discussed.

20. Fractional Order Element Based Impedance Matching

KAUST Repository

2014-06-24

Disclosed are various embodiments of methods and systems related to fractional order element based impedance matching. In one embodiment, a method includes aligning a traditional Smith chart (|.alpha.|=1) with a fractional order Smith chart (|.alpha.|.noteq.1). A load impedance is located on the traditional Smith chart and projected onto the fractional order Smith chart. A fractional order matching element is determined by transitioning along a matching circle of the fractional order Smith chart based at least in part upon characteristic line impedance. In another embodiment, a system includes a fractional order impedance matching application executed in a computing device. The fractional order impedance matching application includes logic that obtains a first set of Smith chart coordinates at a first order, determines a second set of Smith chart coordinates at a second order, and determines a fractional order matching element from the second set of Smith chart coordinates.

1. Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation

Science.gov (United States)

Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin

2017-12-01

Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.

2. Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

Science.gov (United States)

2011-04-01

One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

3. Fractional order junctions

Science.gov (United States)

2015-01-01

Gottfried Leibniz generalized the derivation and integration, extending the operators from integer up to real, or even complex, orders. It is presently recognized that the resulting models capture long term memory effects difficult to describe by classical tools. Leon Chua generalized the set of lumped electrical elements that provide the building blocks in mathematical models. His proposal of the memristor and of higher order elements broadened the scope of variables and relationships embedded in the development of models. This paper follows the two directions and proposes a new logical step, by generalizing the concept of junction. Classical junctions interconnect system elements using simple algebraic restrictions. Nevertheless, this simplistic approach may be misleading in the presence of unexpected dynamical phenomena and requires including additional "parasitic" elements. The novel γ -junction includes, as special cases, the standard series and parallel connections and allows a new degree of freedom when building models. The proposal motivates the search for experimental and real world manifestations of the abstract conjectures.

4. Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems

Directory of Open Access Journals (Sweden)

Leipo Liu

2017-01-01

Full Text Available The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS. Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed method.

5. Development of a novel disturbance observer based fractional order PD controller for a gun control system.

Science.gov (United States)

Gao, Qiang; Zheng, Liang; Chen, Jilin; Wang, Li; Hou, Yuanlong

2014-01-01

Motion control of gun barrels is an ongoing topic for the development of gun control equipment (GCE) with excellent performances. In this paper, a novel disturbance observer (DOB) based fractional order PD (FOPD) control strategy is proposed for the GCE. By adopting the DOB, the control system behaves as if it were the nominal closed-loop system in the absence of disturbances and uncertainties. The optimal control parameters of the FOPD are determined from the loop-shaping perspective, and the Q-filter of the DOB is deliberately designed with consideration of system robustness. The linear frame of the proposed control system will enable the analysis process more convenient. The disturbance rejection properties and the tracking performances of the control system are investigated by both numerical and experimental tests, the results demonstrate that the proposed DOB based FOPD control system is of more robustness, and it is much more suitable for the gun control system with strong nonlinearity and disturbance.

6. A New Fractional-Order Based Intelligent Maximum Power Point Tracking Control Algorithm for Photovoltaic Power Systems

Directory of Open Access Journals (Sweden)

Kuo-Nan Yu

2015-01-01

Full Text Available This paper proposes a new type of variable fractional-order incremental conductance algorithm (VFOINC, combined with extenics variable step size (EVSS control into the maximum power point tracking (MPPT design for photovoltaic power systems. At the beginning of maximum power tracking, the fractional-order number α is selected as 1; the good transient tracking characteristic of traditional incremental conductance method is used. When the maximum power point is approached, the fractional-order number α is selected as variable fractional order; the curve profile of α in fractional order is used to approximate, so that the system has good tracking effect in transient and steady states. The experimental and simulation results show that, compared with traditional incremental conductance method (INC and fractional-order incremental conductance method (FOINC, this method has better MPPT effect.

7. A novel adaptive-impulsive synchronization of fractional-order chaotic systems

Science.gov (United States)

Leung, Y. T. Andrew; Li, Xian-Feng; Chu, Yan-Dong; Zhang, Hui

2015-10-01

A novel adaptive-impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors’ bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive-impulsive control scheme. Project supported by the National Natural Science Foundations of China (Grant Nos. 11161027 and 11262009), the Key Natural Science Foundation of Gansu Province, China (Grant No. 1104WCGA195), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20136204110001).

8. A Novel Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System and DNA Computing

Directory of Open Access Journals (Sweden)

Taiyong Li

2017-01-01

Full Text Available In the era of the Internet, image encryption plays an important role in information security. Chaotic systems and DNA operations have been proven to be powerful for image encryption. To further enhance the security of image, in this paper, we propose a novel algorithm that combines the fractional-order hyperchaotic Lorenz system and DNA computing (FOHCLDNA for image encryption. Specifically, the algorithm consists of four parts: firstly, we use a fractional-order hyperchaotic Lorenz system to generate a pseudorandom sequence that will be utilized during the whole encryption process; secondly, a simple but effective diffusion scheme is performed to spread the little change in one pixel to all the other pixels; thirdly, the plain image is encoded by DNA rules and corresponding DNA operations are performed; finally, global permutation and 2D and 3D permutation are performed on pixels, bits, and acid bases. The extensive experimental results on eight publicly available testing images demonstrate that the encryption algorithm can achieve state-of-the-art performance in terms of security and robustness when compared with some existing methods, showing that the FOHCLDNA is promising for image encryption.

9. A New Fractional-Order Based Intelligent Maximum Power Point Tracking Control Algorithm for Photovoltaic Power Systems

OpenAIRE

Yu, Kuo-Nan; Liao, Chih-Kang; Yau, Her-Terng

2015-01-01

This paper proposes a new type of variable fractional-order incremental conductance algorithm (VFOINC), combined with extenics variable step size (EVSS) control into the maximum power point tracking (MPPT) design for photovoltaic power systems. At the beginning of maximum power tracking, the fractional-order number α is selected as 1; the good transient tracking characteristic of traditional incremental conductance method is used. When the maximum power point is approached, the fractional-ord...

10. Third-order cumulants based method for continuous-time errors-in-variables system identification by fractional models

International Nuclear Information System (INIS)

Chetoui, Manel; Malti, Rachid; Thomassin, Magalie; Aoun, Mohamed; Najar, Slah; Abdelkrim, Naceur

2011-01-01

This paper deals with continuous-time system identification using fractional models in a noisy input/output context. The third-order cumulants based least squares method (tocls) is extended here to fractional models. The derivatives of the third-order cumulants are computed using a new fractional state variable filter. A numerical example is used to demonstrate the performance of the proposed method called ftocls (fractional third-order cumulants based least squares). The effect of the signal-to-noise ratio and the hyperparameter is studied.

11. Multiobjective optimization design of a fractional order PID controller for a gun control system.

Science.gov (United States)

Gao, Qiang; Chen, Jilin; Wang, Li; Xu, Shiqing; Hou, Yuanlong

2013-01-01

Motion control of gun barrels is an ongoing topic for the development of gun control equipments possessing excellent performances. In this paper, a typical fractional order PID control strategy is employed for the gun control system. To obtain optimal parameters of the controller, a multiobjective optimization scheme is developed from the loop-shaping perspective. To solve the specified nonlinear optimization problem, a novel Pareto optimal solution based multiobjective differential evolution algorithm is proposed. To enhance the convergent rate of the optimization process, an opposition based learning method is embedded in the chaotic population initialization process. To enhance the robustness of the algorithm for different problems, an adapting scheme of the mutation operation is further employed. With assistance of the evolutionary algorithm, the optimal solution for the specified problem is selected. The numerical simulation results show that the control system can rapidly follow the demand signal with high accuracy and high robustness, demonstrating the efficiency of the proposed controller parameter tuning method.

12. Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO.

Science.gov (United States)

Pan, Indranil; Das, Saptarshi

2016-05-01

This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

13. Ferroelectric Fractional-Order Capacitors

KAUST Repository

Agambayev, Agamyrat

2017-07-25

Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

14. A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations

International Nuclear Information System (INIS)

Zhang Li-Min; Sun Ke-Hui; Liu Wen-Hao; He Shao-Bo

2017-01-01

In this paper, Adomian decomposition method (ADM) with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear (PWL) hyperchaotic system. Based on the obtained hyperchaotic sequences, a novel color image encryption algorithm is proposed by employing a hybrid model of bidirectional circular permutation and DNA masking. In this scheme, the pixel positions of image are scrambled by circular permutation, and the pixel values are substituted by DNA sequence operations. In the DNA sequence operations, addition and substraction operations are performed according to traditional addition and subtraction in the binary, and two rounds of addition rules are used to encrypt the pixel values. The simulation results and security analysis show that the hyperchaotic map is suitable for image encryption, and the proposed encryption algorithm has good encryption effect and strong key sensitivity. It can resist brute-force attack, statistical attack, differential attack, known-plaintext, and chosen-plaintext attacks. (paper)

15. A new color image encryption scheme using CML and a fractional-order chaotic system.

Directory of Open Access Journals (Sweden)

Xiangjun Wu

Full Text Available The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks.

16. Variable-order fuzzy fractional PID controller.

Science.gov (United States)

Liu, Lu; Pan, Feng; Xue, Dingyu

2015-03-01

In this paper, a new tuning method of variable-order fractional fuzzy PID controller (VOFFLC) is proposed for a class of fractional-order and integer-order control plants. Fuzzy logic control (FLC) could easily deal with parameter variations of control system, but the fractional-order parameters are unable to change through this way and it has confined the effectiveness of FLC. Therefore, an attempt is made in this paper to allow all the five parameters of fractional-order PID controller vary along with the transformation of system structure as the outputs of FLC, and the influence of fractional orders λ and μ on control systems has been investigated to make the fuzzy rules for VOFFLC. Four simulation results of different plants are shown to verify the availability of the proposed control strategy. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

17. Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System

Science.gov (United States)

Ma, Junhai; Ren, Wenbo

On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.

18. Multiobjective Optimization Design of a Fractional Order PID Controller for a Gun Control System

Directory of Open Access Journals (Sweden)

Qiang Gao

2013-01-01

Full Text Available Motion control of gun barrels is an ongoing topic for the development of gun control equipments possessing excellent performances. In this paper, a typical fractional order PID control strategy is employed for the gun control system. To obtain optimal parameters of the controller, a multiobjective optimization scheme is developed from the loop-shaping perspective. To solve the specified nonlinear optimization problem, a novel Pareto optimal solution based multiobjective differential evolution algorithm is proposed. To enhance the convergent rate of the optimization process, an opposition based learning method is embedded in the chaotic population initialization process. To enhance the robustness of the algorithm for different problems, an adapting scheme of the mutation operation is further employed. With assistance of the evolutionary algorithm, the optimal solution for the specified problem is selected. The numerical simulation results show that the control system can rapidly follow the demand signal with high accuracy and high robustness, demonstrating the efficiency of the proposed controller parameter tuning method.

19. Intermediate Symmetries in Electronic Systems:. Dimensional Reduction, Order Out of Disorder, Dualities, and Fractionalization

Science.gov (United States)

Nussinov, Zohar; Batista, Cristian D.; Fradkin, Eduardo

2006-09-01

We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall systems, transition metal orbital systems, frustrated spin systems, (p+ip) superconducting arrays, and sliding Luttinger liquids. By considering space-time reflection symmetries, we illustrate that several of these systems are dual to each other. In some systems exhibiting these symmetries, low temperature local orders emerge by an "order out of disorder" effect while in other systems, the dimensional reduction precludes standard orders yet allows for multiparticle orders (including those of a topological nature).

20. Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

Science.gov (United States)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

1. Fractional Processes and Fractional-Order Signal Processing Techniques and Applications

CERN Document Server

Sheng, Hu; Qiu, TianShuang

2012-01-01

Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: • presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; • introduces FOSP techniques and the fractional signals and fractional systems point of view; • details real-world-application examples of FOSP techniques to demonstr...

2. Dynamical Analysis on Single Degree-of-Freedom Semiactive Control System by Using Fractional-Order Derivative

Directory of Open Access Journals (Sweden)

Yongjun Shen

2015-01-01

Full Text Available The single degree-of-freedom (SDOF system under the control of three semiactive methods is analytically studied in this paper, where a fractional-order derivative is used in the mathematical model. The three semiactive control methods are on-off control, limited relative displacement (LRD control, and relative control, respectively. The averaging method is adopted to provide an analytical study on the performance of the three different control methods. Based on the comparison between the analytical solutions with the numerical ones, it could be proved that the analytical solutions are accurate enough. The effects of the fractional-order parameters on the control performance, especially the relative and absolute displacement transmissibility, are analyzed. The research results indicate that the steady-state amplitudes of the three semiactive systems with fractional-order derivative in the model could be significantly reduced and the control performance can be greatly improved.

3. ℋ∞ Adaptive observer for nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima

2016-06-23

In this paper, an adaptive observer is proposed for the joint estimation of states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü\\'s systems. © 2016 John Wiley & Sons, Ltd.

4. Hyperchaotic Chameleon: Fractional Order FPGA Implementation

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Karthikeyan Rajagopal

2017-01-01

Full Text Available There are many recent investigations on chaotic hidden attractors although hyperchaotic hidden attractor systems and their relationships have been less investigated. In this paper, we introduce a hyperchaotic system which can change between hidden attractor and self-excited attractor depending on the values of parameters. Dynamic properties of these systems are investigated. Fractional order models of these systems are derived and their bifurcation with fractional orders is discussed. Field programmable gate array (FPGA implementations of the systems with their power and resource utilization are presented.

5. Energy Management System Based on Fuzzy fractional order PID Controller for Transient Stability Improvement in Microgrids with Energy Storage

DEFF Research Database (Denmark)

Moafi, Milad; Marzband, Mousa; Savaghebi, Mehdi

2016-01-01

in the islanded Microgrid (MG). To increase performance for a wide range of power system operating conditions, an energy management systems (EMS) is proposed based on a fuzzy fractional order PID (FFOPID) controller. It is able to analyze and simulate the dynamic behavior in grid connected MGs. This controller...... combined with a PID-controller (termed as FLPID) and Fuzzy fractional order PID (termed as FFOPID) are implemented according to the characteristics and limitations of overloading and state of charge (SOC). The obtained results show good performance of FFOPID controllers by improving the transient stability...... following a fault that has caused the islanded operation. Simulation results have validated the effectiveness of FFOPID controllers in the system under several scenarios with superior stabilization and more robustness in comparison with the FLPID and PID controller....

6. Fractional-order control and simulation of wind energy systems with PMSG/full-power converter topology

Energy Technology Data Exchange (ETDEWEB)

Melicio, R.; Catalao, J.P.S. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)

2010-06-15

This paper presents a new integrated model for the simulation of wind energy systems. The proposed model is more realistic and accurate, considering a variable-speed wind turbine, two-mass rotor, permanent magnet synchronous generator (PMSG), different power converter topologies, and filters. Additionally, a new control strategy is proposed for the variable-speed operation of wind turbines with PMSG/full-power converter topology, based on fractional-order controllers. Comprehensive simulation studies are carried out with matrix and multilevel power converter topologies, in order to adequately assert the system performance in what regards the quality of the energy injected into the electric grid. Finally, conclusions are duly drawn. (author)

7. Fractional Order PID Controller Design for Level Control of Three Tank System Based on Improved Cuckoo Optimization Algorithm

Directory of Open Access Journals (Sweden)

2015-01-01

Full Text Available Fractional-order PID (FOPID controller is a generalization of standard PID controller using fractional calculus. Compared with the Standard PID controller, two adjustable variables “differential order” and “integral order” are added to the PID controller.Three tank system is a nonlinear multivariable process that is a good prototype of chemical industrial processes. Cuckoo Optimization Algorithm (COA, that was recently introduced has shown its good performance in optimization problems. In this study, Improved Cuckoo Optimization Algorithm (ICOA has been presented. The aim of the paper is to compare different controllers tuned with a Improved Cuckoo Optimization Algorithm (ICOA for Three Tank System. In order to compare the performance of the optimized FOPID controller with other controllers, Genetic Algorithm(GA, Particle swarm optimization (PSO, Cuckoo Optimization Algorithm (COA and Imperialist Competitive Algorithm (ICA.

8. Applying novel fractional order incremental conductance algorithm to design and study the maximum power tracking of small wind power systems

OpenAIRE

Yu, Kuo Nan; Liao, Chih Kang

2015-01-01

The maximum power point tracking is a very important scheme of many renewable energy. It can increase the power efficiency. However, many traditional methods has defects for the applications. This study proposed a novel fractional order incremental conductance algorithm (FOINC) for the maximum power point tracking design of small wind power systems. The proposed method is prompt in the transient of maximum power point tracking and has good steady-state response. Moreover, it can increase the ...

9. Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers

Directory of Open Access Journals (Sweden)

S Saha Ray

2016-05-01

Full Text Available This article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of fractional derivative varies continuously. Here, we handle the continuous changing nature of fractional order derivative for dynamic systems, which has not been studied yet. By successive recursive method, here we find the solution of fractional continuously variable order mass–spring–damper systems and then obtain closed-form solutions. We then present and discuss the solutions obtained in the cases with continuously variable order of damping for oscillator through graphical plots.

10. Modified Projective Synchronization between Different Fractional-Order Systems Based on Open-Plus-Closed-Loop Control and Its Application in Image Encryption

Directory of Open Access Journals (Sweden)

Hongjuan Liu

2014-01-01

Full Text Available A new general and systematic coupling scheme is developed to achieve the modified projective synchronization (MPS of different fractional-order systems under parameter mismatch via the Open-Plus-Closed-Loop (OPCL control. Based on the stability theorem of linear fractional-order systems, some sufficient conditions for MPS are proposed. Two groups of numerical simulations on the incommensurate fraction-order system and commensurate fraction-order system are presented to justify the theoretical analysis. Due to the unpredictability of the scale factors and the use of fractional-order systems, the chaotic data from the MPS is selected to encrypt a plain image to obtain higher security. Simulation results show that our method is efficient with a large key space, high sensitivity to encryption keys, resistance to attack of differential attacks, and statistical analysis.

11. Few Fractional Order Derivatives and Their Computations

Science.gov (United States)

Bhatta, D. D.

2007-01-01

This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

12. Synchronization of two coupled fractional-order chaotic oscillators

International Nuclear Information System (INIS)

Gao Xin; Yu, Juebang

2005-01-01

The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, the synchronization of two coupled nonlinear fractional order chaotic oscillators is numerically demonstrated using the master-slave synchronization scheme. It is shown that fractional-order chaotic oscillators can be synchronized with appropriate coupling strength

13. Q-S synchronization of the fractional-order unified system

2013-03-03

Mar 3, 2013 ... elastic systems, quantitative finance, bioengineering, diffusion wave and nuclear magnetic resonance [1–4]. Its advantage lies in providing an excellent instrument for the description of memory and hereditary properties of various materials and processes. Recently, many authors begin to investigate the ...

14. Development of a Fractional Order Chaos Synchronization Dynamic Error Detector for Maximum Power Point Tracking of Photovoltaic Power Systems

Directory of Open Access Journals (Sweden)

Kuo-Nan Yu

2015-11-01

Full Text Available In recent years, the photovoltaic (PV power generation system has been widely discussed and researched. Research on electric energy focuses on the development of Maximum Power Point Tracking (MPPT technology, and many methods have been proposed. However, these studies have a common defect: the tracking continues near the maximum power point (MPP, so that the waveform of output power jitters, thus causing power loss and rapid wearing of electronic modules. In order to remedy this defect, this paper proposes a new type of fractional order chaos synchronization dynamic error detector for the MPPT design of a PV power system. In this study, the Sprott chaos synchronization dynamic error system was used to control the pulse width duty cycle of PWM and optimize the power oscillation of a PV power system during steady-state response. The simulation and experimental results showed that the voltage detector proposed in this paper can reduce the power oscillation of a PV power system during steady-state response, and increase the overall system efficiency. From the steady-state responses of MPPT, it can be seen that about 0.2 vibration amplitude can be suppressed with control action. Therefore, about 4% of steady-state vibration energy can be saved.

15. Extended state observer–based fractional order proportional–integral–derivative controller for a novel electro-hydraulic servo system with iso-actuation balancing and positioning

Directory of Open Access Journals (Sweden)

Qiang Gao

2015-12-01

Full Text Available Aiming at balancing and positioning of a new electro-hydraulic servo system with iso-actuation configuration, an extended state observer–based fractional order proportional–integral–derivative controller is proposed in this study. To meet the lightweight requirements of heavy barrel weapons with large diameters, an electro-hydraulic servo system with a three-chamber hydraulic cylinder is especially designed. In the electro-hydraulic servo system, the balance chamber of the hydraulic cylinder is used to realize active balancing of the unbalanced forces, while the driving chambers consisting of the upper and lower chambers are adopted for barrel positioning and dynamic compensation of external disturbances. Compared with conventional proportional–integral–derivative controllers, the fractional order proportional–integral–derivative possesses another two adjustable parameters by expanding integer order to arbitrary order calculus, resulting in more flexibility and stronger robustness of the control system. To better compensate for strong external disturbances and system nonlinearities, the extended state observer strategy is further introduced to the fractional order proportional–integral–derivative control system. Numerical simulation and bench test indicate that the extended state observer–based fractional order proportional–integral–derivative significantly outperforms proportional–integral–derivative and fractional order proportional–integral–derivative control systems with better control accuracy and higher system robustness, well demonstrating the feasibility and effectiveness of the proposed extended state observer–based fractional order proportional–integral–derivative control strategy.

16. Dynamical models of happiness with fractional order

Science.gov (United States)

Song, Lei; Xu, Shiyun; Yang, Jianying

2010-03-01

This present study focuses on a dynamical model of happiness described through fractional-order differential equations. By categorizing people of different personality and different impact factor of memory (IFM) with different set of model parameters, it is demonstrated via numerical simulations that such fractional-order models could exhibit various behaviors with and without external circumstance. Moreover, control and synchronization problems of this model are discussed, which correspond to the control of emotion as well as emotion synchronization in real life. This study is an endeavor to combine the psychological knowledge with control problems and system theories, and some implications for psychotherapy as well as hints of a personal approach to life are both proposed.

17. Optimal design and tuning of novel fractional order PID power system stabilizer using a new metaheuristic Bat algorithm

Directory of Open Access Journals (Sweden)

Lakhdar Chaib

2017-06-01

Full Text Available This paper proposes a novel robust power system stabilizer (PSS, based on hybridization of fractional order PID controller (PIλDμ and PSS for optimal stabilizer (FOPID-PSS for the first time, using a new metaheuristic optimization Bat algorithm (BA inspired by the echolocation behavior to improve power system stability. The problem of FOPID-PSS design is transformed as an optimization problem based on performance indices (PI, including Integral Absolute Error (IAE, Integral Squared Error (ISE, Integral of the Time-Weighted Absolute Error (ITAE and Integral of Time multiplied by the Squared Error (ITSE, where, BA is employed to obtain the optimal stabilizer parameters. In order to examine the robustness of FOPID-PSS, it has been tested on a Single Machine Infinite Bus (SMIB power system under different disturbances and operating conditions. The performance of the system with FOPID-PSS controller is compared with a PID-PSS and PSS. Further, the simulation results obtained with the proposed BA based FOPID-PSS are compared with those obtained with FireFly algorithm (FFA based FOPID-PSS. Simulation results show the effectiveness of BA for FOPID-PSS design, and superior robust performance for enhancement power system stability compared to other with different cases.

18. On some fractional order hardy inequalities

Directory of Open Access Journals (Sweden)

1997-01-01

Full Text Available Weighted inequalities for fractional derivatives (= fractional order Hardy-type inequalities have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.

19. On some fractional order hardy inequalities

Directory of Open Access Journals (Sweden)

Kufner Alois

1997-01-01

Full Text Available Weighted inequalities for fractional derivatives ( fractional order Hardy-type inequalities have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.

20. Approximated Fractional Order Chebyshev Lowpass Filters

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Todd Freeborn

2015-01-01

Full Text Available We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of (1+α, (2+α, and (3+α order lowpass filters with fractional steps from α = 0.1 to α = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits.

1. On Fractional Order Hybrid Differential Equations

Directory of Open Access Journals (Sweden)

Mohamed A. E. Herzallah

2014-01-01

Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

2. Dynamic analysis with a fractional-order chaotic system for estimation of peripheral arterial disease in diabetic foot

International Nuclear Information System (INIS)

Li, Chien-Ming; Wu, Jian-Xing; Chen, Tainsong; Du, Yi-Chun; Lin, Chia-Hung; Ho, Yueh-Ren

2013-01-01

Lower-extremity peripheral arterial disease (PAD) is caused by narrowing or occlusion of vessels in patients like type 2 diabetes mellitus, the elderly and smokers. Patients with PAD are mostly asymptomatic; typical early symptoms of this limb-threatening disorder are intermittent claudication and leg pain, suggesting the necessity for accurate diagnosis by invasive angiography and ankle-brachial pressure index. This index acts as a gold standard reference for PAD diagnosis and categorizes its severity into normal, low-grade and high-grade, with respective cut-off points of ≥0.9, 0.9–0.5 and <0.5. PAD can be assessed using photoplethysmography as a diagnostic screening tool, displaying changes in pulse transit time and shape, and dissimilarities of these changes between lower limbs. The present report proposed photoplethysmogram with fractional-order chaotic system to assess PAD in 14 diabetics and 11 healthy adults, with analysis of dynamic errors based on various butterfly motion patterns, and color relational analysis as classifier for pattern recognition. The results show that the classification of PAD severity among these testees was achieved with high accuracy and efficiency. This noninvasive methodology potentially provides timing and accessible feedback to patients with asymptomatic PAD and their physicians for further invasive diagnosis or strict management of risk factors to intervene in the disease progression. (paper)

3. Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system

Science.gov (United States)

2018-03-01

In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal auto-catalytic chemical system (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q -homotopy analysis transform method ( q -HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h , the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.

4. Anomalous Symmetry Fractionalization and Surface Topological Order

Directory of Open Access Journals (Sweden)

Xie Chen

2015-10-01

Full Text Available In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain “anomalous” SETs can only occur on the surface of a 3D symmetry-protected topological (SPT phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H^{4}(G,U(1, which also precisely labels the set of 3D SPT phases, with symmetry group G. An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U(1_{2}] topological order with a reduced symmetry Z_{2}×Z_{2}⊂SO(3, which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.

5. Tunable fractional-order Fourier transformer

International Nuclear Information System (INIS)

Malyutin, A A

2006-01-01

A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

6. Adaptive control and synchronization of a fractional-order chaotic ...

tem based on the stability theory of fractional-order dynamic systems. The presented schemes, which contain only a single-state variable, are simple and flexible. Numerical simulations are used to demonstrate the feasibility of the presented methods. Keywords. Fractional order; adaptive scheme; control; synchronization.

7. Fractional-order RC and RL circuits

KAUST Repository

2012-05-30

This paper is a step forward to generalize the fundamentals of the conventional RC and RL circuits in fractional-order sense. The effect of fractional orders is the key factor for extra freedom, more flexibility, and novelty. The conditions for RC and RL circuits to act as pure imaginary impedances are derived, which are unrealizable in the conventional case. In addition, the sensitivity analyses of the magnitude and phase response with respect to all parameters showing the locations of these critical values are discussed. A qualitative revision for the fractional RC and RL circuits in the frequency domain is provided. Numerical and PSpice simulations are included to validate this study. © Springer Science+Business Media, LLC 2012.

8. Higher Order and Fractional Diffusive Equations

Directory of Open Access Journals (Sweden)

D. Assante

2015-07-01

Full Text Available We discuss the solution of various generalized forms of the Heat Equation, by means of different tools ranging from the use of Hermite-Kampé de Fériet polynomials of higher and fractional order to operational techniques. We show that these methods are useful to obtain either numerical or analytical solutions.

9. Fractional-Order Control of Pneumatic Position Servosystems

Directory of Open Access Journals (Sweden)

Cao Junyi

2011-01-01

Full Text Available A fractional-order control strategy for pneumatic position servosystem is presented in this paper. The idea of the fractional calculus application to control theory was introduced in many works, and its advantages were proved. However, the realization of fractional-order controllers for pneumatic position servosystems has not been investigated. Based on the relationship between the pressure in cylinder and the rate of mass flow into the cylinder, the dynamic model of pneumatic position servo system is established. The fractional-order controller for pneumatic position servo and its implementation in industrial computer is designed. The experiments with fractional-order controller are carried out under various conditions, which include sine position signal with different frequency and amplitude, step position signal, and variety inertial load. The results show the effectiveness of the proposed scheme and verify their fine control performance for pneumatic position servo system.

10. Fractional-order in a macroeconomic dynamic model

Science.gov (United States)

David, S. A.; Quintino, D. D.; Soliani, J.

2013-10-01

In this paper, we applied the Riemann-Liouville approach in order to realize the numerical simulations to a set of equations that represent a fractional-order macroeconomic dynamic model. It is a generalization of a dynamic model recently reported in the literature. The aforementioned equations have been simulated for several cases involving integer and non-integer order analysis, with some different values to fractional order. The time histories and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the macroeconomic dynamic model proposed here involves the public sector deficit equation, which renders the model more realistic and complete when compared with the ones encountered in the literature. The results reveal that the fractional-order macroeconomic model can exhibit a real reasonable behavior to macroeconomics systems and might offer greater insights towards the understanding of these complex dynamic systems.

11. FPGA implementation of fractional-order discrete memristor chaotic ...

Anitha Karthikeyan

2017-12-30

Dec 30, 2017 ... ing DDR clocks help in reducing the route delays. 7. Conclusions. In this paper, we investigated the discrete fractional- order model of a fourth-order memristor chaotic system. The discrete model is formed by transforming the dif- ferential version of the system using finite truncation method. The Lyapunov ...

12. Leader-following exponential consensus of fractional order nonlinear multi-agents system with hybrid time-varying delay: A heterogeneous impulsive method

Science.gov (United States)

Wang, Fei; Yang, Yongqing

2017-09-01

In this paper, we study the leader-following exponential consensus of multi-agent system. Each agent in the system is described by nonlinear fractional order differential equation. Both the internal delay and coupling delay are taken into consideration. The heterogeneous impulsive control is used for ensuring the consensus of all agents. Based on Lyapunov function method and matrix analysis, some sufficient conditions for exponential consensus are obtained. Finally, some illustrative examples are given to show the effectiveness of the obtained results.

13. Introducing the fractional order robotic Darwinian PSO

Science.gov (United States)

Couceiro, Micael S.; Martins, Fernando M. L.; Rocha, Rui P.; Ferreira, Nuno M. F.

2012-11-01

The Darwinian Particle Swarm Optimization (DPSO) is an evolutionary algorithm that extends the Particle Swarm Optimization using natural selection to enhance the ability to escape from sub-optimal solutions. An extension of the DPSO to multi-robot applications has been recently proposed and denoted as Robotic Darwinian PSO (RDPSO), benefiting from the dynamical partitioning of the whole population of robots, hence decreasing the amount of required information exchange among robots. This paper further extends the previously proposed algorithm using fractional calculus concepts to control the convergence rate, while considering the robot dynamical characteristics. Moreover, to improve the convergence analysis of the RDPSO, an adjustment of the fractional coefficient based on mobile robot constraints is presented and experimentally assessed with 2 real platforms. Afterwards, this novel fractional-order RDPSO is evaluated in 12 physical robots being further explored using a larger population of 100 simulated mobile robots within a larger scenario. Experimental results show that changing the fractional coefficient does not significantly improve the final solution but presents a significant influence in the convergence time because of its inherent memory property.

14. Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations

Directory of Open Access Journals (Sweden)

2017-01-01

Full Text Available We established the theory to coupled systems of multipoints boundary value problems of fractional order hybrid differential equations with nonlinear perturbations of second type involving Caputo fractional derivative. The proposed problem is as follows: D cαxt-ft,xt=gt,yt,Iαyt, t∈J=[0,1],D cαyt-ft,yt=gt,xt,Iαxt, t∈J=0,1, D cpx0=ψxη1, x′0=0,…,xn-20=0, D cpx1=ψxη2, D cpy0=ψyη1, y′0=0,…,yn-20=0, D cpy1=ψyη2, where p,η1,η2∈0,1, ψ is linear, D cα is Caputo fractional derivative of order α, with n-1<α≤n, n∈N, and Iα is fractional integral of order α. The nonlinear functions f, g are continuous. For obtaining sufficient conditions on existence and uniqueness of positive solutions to the above system, we used the technique of topological degree theory. Finally, we illustrated the main results by a concrete example.

15. Stability analysis of fractional-order generalized chaotic susceptible ...

tious diseases which can eventually be used to predict the future course of outbreak and to evaluate strategies to ... dynamics are some suitable forms of describing the biological systems using the language of dynamical ... matical modelling by replacing first-order derivatives by fractional derivative of order α (0 < α ≤ 1).

16. The synchronization of three fractional differential systems

International Nuclear Information System (INIS)

Li Changpin; Yan Jianping

2007-01-01

In this paper, a new method is proposed and applied to the synchronization of fractional differential systems (or 'differential systems with fractional orders'), where both drive and response systems have the same dimensionality and are coupled by the driving signal. The present technique is based on the stability criterion of linear fractional systems. This method is implemented in (chaos) synchronization of the fractional Lorenz system, Chen system and Chua circuit. Numerical simulations show the present synchronization method works well

17. Fractional Order Signal Processing Introductory Concepts and Applications

CERN Document Server

Das, Saptarshi

2012-01-01

The book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. This book is aimed at postgraduate and beginning level research scholars who would like to work in the field of Fractional Order Signal processing (FOSP). The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in connection to the appropriate signal processing topics. Basic signal processing techniques like filtering, estimation, system identification, etc. in the light of fractional order calculus are presented along with relevant application areas. The readers can easily extend these concepts to varied disciplines like image or speech processing, pattern recognition, time series forecasting, financial data analysis and modeling, traffic modeling in communication channels, optics, b...

18. Fractional-Order Modeling and Sliding Mode Control of Energy-Saving and Emission-Reduction Dynamic Evolution System

DEFF Research Database (Denmark)

Huang, Sunhua; Zhou, Bin; Li, Canbing

2018-01-01

represent complex dynamic behaviours with chaotic and unstable states on the energy conservation, carbon emissions, economic growth, and renewable energy development, and have a great impact on the formulation of government energy policies. Furthermore, based on the fractional Lyapunov stability and robust...

19. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

Directory of Open Access Journals (Sweden)

Ahmed HamdyM

2010-01-01

Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

20. Continuous fractional-order Zero Phase Error Tracking Control.

Science.gov (United States)

Liu, Lu; Tian, Siyuan; Xue, Dingyu; Zhang, Tao; Chen, YangQuan

2018-02-16

A continuous time fractional-order feedforward control algorithm for tracking desired time varying input signals is proposed in this paper. The presented controller cancels the phase shift caused by the zeros and poles of controlled closed-loop fractional-order system, so it is called Fractional-Order Zero Phase Tracking Controller (FZPETC). The controlled systems are divided into two categories i.e. with and without non-cancellable (non-minimum-phase) zeros which stand in unstable region or on stability boundary. Each kinds of systems has a targeted FZPETC design control strategy. The improved tracking performance has been evaluated successfully by applying the proposed controller to three different kinds of fractional-order controlled systems. Besides, a modified quasi-perfect tracking scheme is presented for those systems which may not have available future tracking trajectory information or have problem in high frequency disturbance rejection if the perfect tracking algorithm is applied. A simulation comparison and a hardware-in-the-loop thermal peltier platform are shown to validate the practicality of the proposed quasi-perfect control algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

1. Adaptive control and synchronization of a fractional-order chaotic ...

journal of. April 2013 physics pp. 583–592. Adaptive control and synchronization of a fractional-order chaotic system. CHUNLAI LI1,∗ and YAONAN TONG2. 1College of Physics and Electronics; 2School of Information and Communication Engineering,. Hunan Institute of Science and Technology, Yueyang 414006, China.

2. ℋ− adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima

2014-12-01

In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown parameters are also adapted to their values. Sufficient conditions for the stability of the adaptive observer error dynamics are derived in terms of linear matrix inequalities. Simulation results for chaotic Lorenz systems with unknown parameters in the presence of external perturbations are given to illustrate the effectiveness of our proposed approach. © 2014 IEEE.

3. Research on Modeling of Hydropneumatic Suspension Based on Fractional Order

Directory of Open Access Journals (Sweden)

Junwei Zhang

2015-01-01

Full Text Available With such excellent performance as nonlinear stiffness, adjustable vehicle height, and good vibration resistance, hydropneumatic suspension (HS has been more and more applied to heavy vehicle and engineering vehicle. Traditional modeling methods are still confined to simple models without taking many factors into consideration. A hydropneumatic suspension model based on fractional order (HSM-FO is built with the advantage of fractional order (FO in viscoelastic material modeling considering the mechanics property of multiphase medium of HS. Then, the detailed calculation method is proposed based on Oustaloup filtering approximation algorithm. The HSM-FO is implemented in Matlab/Simulink, and the results of comparison among the simulation curve of fractional order, integral order, and the curve of real experiment prove the feasibility and validity of HSM-FO. The damping force property of the suspension system under different fractional orders is also studied. In the end of this paper, several conclusions concerning HSM-FO are drawn according to analysis of simulation.

4. Robust Synchronization of Fractional-Order Chaotic Systems at a Pre-Specified Time Using Sliding Mode Controller with Time-Varying Switching Surfaces

International Nuclear Information System (INIS)

2016-01-01

A main problem associated with the synchronization of two chaotic systems is that the time in which complete synchronization will occur is not specified. Synchronization time is either infinitely large or is finite but only its upper bound is known and this bound depends on the systems' initial conditions. In this paper we propose a method for synchronizing of two chaotic systems precisely at a time which we want. To this end, time-varying switching surfaces sliding mode control is used and the control law based on Lyapunov stability theorem is derived which is able to synchronize two fractional-order chaotic systems precisely at a pre specified time without concerning about their initial conditions. Moreover, by eliminating the reaching phase in the proposed synchronization scheme, robustness against existence of uncertainties and exogenous disturbances is obtained. Because of the existence of fractional integral of the sign function instead of the sign function in the control equation, the necessity for infinitely fast switching be obviated in this method. To show the effectiveness of the proposed method the illustrative examples under different situations are provided and the simulation results are reported.

5. Applying fractional order PID to design TCSC-based damping controller in coordination with automatic generation control of interconnected multi-source power system

Directory of Open Access Journals (Sweden)

2017-02-01

Full Text Available In this paper, fractional order proportional-integral-differential (FOPID controller is employed in the design of thyristor controlled series capacitor (TCSC-based damping controller in coordination with the secondary integral controller as automatic generation control (AGC loop. In doing so, the contribution of the TCSC in tie-line power exchange is extracted mathematically for small load disturbance. Adjustable parameters of the proposed FOPID-based TCSC damping controller and the AGC loop are optimized concurrently via an improved particle swarm optimization (IPSO algorithm which is reinforced by chaotic parameter and crossover operator to obtain a globally optimal solution. The powerful FOMCON toolbox is used along with MATLAB for handling fractional order modeling and control. An interconnected multi-source power system is simulated regarding the physical constraints of generation rate constraint (GRC nonlinearity and governor dead band (GDB effect. Simulation results using FOMCON toolbox demonstrate that the proposed FOPID-based TCSC damping controller achieves the greatest dynamic performance under different load perturbation patterns in comparison with phase lead-lag and classical PID-based TCSC damping controllers, all in coordination with the integral AGC. Moreover, sensitivity analyses are performed to show the robustness of the proposed controller under various uncertainty scenarios.

6. A General Method for Designing Fractional Order PID Controller

Directory of Open Access Journals (Sweden)

Marzieh Safaei

2013-01-01

Full Text Available The idea of using fractional order calculus in control became apparent when this kind of calculus was accepted as a powerful tool in many applications. This resulted in a new generation of PID controller called fractional order PID Controller, named as Controller. controller is more flexible and provides a better response with larger stability region as compared with standard PID controller. This paper presents a simple and reliable method for finding the family of controllers. The required calculations are done in frequency domain based on frequency response of the system and the stability region is specified in the parameters space. This method can be used for time-delay systems and, more generally, for any system with no transfer function.

7. Stability analysis of fractional-order generalized chaotic susceptible ...

ventable childhood diseases can be found in the work of D'Onofrio et al [2]. Simple epidemiological ... of first-order time derivative with a fractional-order time derivative is not only appli- cable for non-Gaussian but ... matical modelling by replacing first-order derivatives by fractional derivative of order α (0 < α ≤ 1). Several ...

8. FPGA implementation of fractional-order discrete memristor chaotic ...

Anitha Karthikeyan

2017-12-30

Dec 30, 2017 ... ential equations are also presented by many researchers. [32–40]. There are many recent ... model of a cubic memristor [29,30], the memductance function is given by. W(φ(t)) = a + 3bφ(t). 2 ,. (2) .... 3D state portraits of the fractional-order discrete memristor system (q = 0.95). z(k + 1) = z(k) + {λy(k) − μz(k) + ...

9. Butterworth passive filter in the fractional-order

KAUST Repository

Sołtan, Ahmed

2011-12-01

In this paper, the generalized analysis of the first Butterworth filter based on two passive elements is introduced in the fractional-order sense. The fractional-order condition of the Butterworth circuit is presented for the first time where it will lead us back to the known condition of the integer-order circuit when the two fractional-orders equal one. Therefore, the conventional behavior of the integer-order circuit is a narrow subset of the fractional-order ones. The circuit is studied under same and different order cases, and verified through their numerical simulations. Stability analysis is also introduced showing the poles location in the fractional-order versus integer order cases. © 2011 IEEE.

10. Electronically Tunable Fully Integrated Fractional-Order Resonator

KAUST Repository

Tsirimokou, Georgia

2017-03-20

A fully integrated implementation of a parallel fractional-order resonator which employs together a fractional order capacitor and a fractional-order inductor is proposed in this paper. The design utilizes current-controlled Operational Transconductance Amplifiers as building blocks, designed and fabricated in AMS 0:35m CMOS process, and based on a second-order approximation of a fractional-order differentiator/ integrator magnitude optimized in the range 10Hz–700Hz. An attractive benefit of the proposed scheme is its electronic tuning capability.

11. Fractional Reserve in Banking System

OpenAIRE

Valkonen, Maria

2016-01-01

This thesis is aimed to provide understanding of the role of the fractional reserve in the mod-ern banking system worldwide and particularly in Finland. The fractional reserve banking is used worldwide, but the benefits of this system are very disputable. On the one hand, experts say that the fractional reserve is a necessary instrument for the normal business and profit making. On the other hand, sceptics openly criticize the fractional reserve system and blame it for fiat money (money n...

12. Position control of an industrial robot using fractional order controller

Science.gov (United States)

2017-02-01

This paper presents the design of a control structure that ensures no overshoot for the movement of an industrial robot, used for the evacuation of round steel blocks from inside a rotary hearth furnace. First, a mathematical model for the positioning system is derived from a set of experimental data, and further, the paper focuses on obtaining a PID type controller, using the relay method as tuning method in order to obtain a stable closed loop system. The controller parameters are further tuned in order to achieve the imposed set of performances for the positioning of the industrial robot through computer simulation, using trial and error method. Further, a fractional - order PID controller is obtained in order to improve the control signal variation, so as to fit within the range of unified current's variation, 4 to 20 mA.

13. On solutions of variable-order fractional differential equations

Directory of Open Access Journals (Sweden)

Ali Akgül

2017-01-01

solutions to fractional differential equations are compelling to get in real applications, due to the nonlocality and complexity of the fractional differential operators, especially for variable-order fractional differential equations. Therefore, it is significant to enhanced numerical methods for fractional differential equations. In this work, we consider variable-order fractional differential equations by reproducing kernel method. There has been much attention in the use of reproducing kernels for the solutions to many problems in the recent years. We give two examples to demonstrate how efficiently our theory can be implemented in practice.

14. Mathematical modelling of fractional order circuit elements and bioimpedance applications

Science.gov (United States)

Moreles, Miguel Angel; Lainez, Rafael

2017-05-01

In this work a classical derivation of fractional order circuits models is presented. Generalised constitutive equations in terms of fractional Riemann-Liouville derivatives are introduced in the Maxwell's equations for each circuit element. Next the Kirchhoff voltage law is applied in a RCL circuit configuration. It is shown that from basic properties of Fractional Calculus, a fractional differential equation model with Caputo derivatives is obtained. Thus standard initial conditions apply. Finally, models for bioimpedance are revisited.

15. Fractional order differentiation by integration with Jacobi polynomials

KAUST Repository

Liu, Dayan

2012-12-01

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

16. Fractional order PID controller for load frequency control

International Nuclear Information System (INIS)

Sondhi, Swati; Hote, Yogesh V.

2014-01-01

Highlights: • The manuscript shows the design of FOPID controller for the load frequency control. • Performance of FOPID is given for non-reheated, reheated and hydro turbine. • Performance of FOPID is compared to IMC-PID and reduced order IMC-PID design scheme. • Performance of FOPID is better than the existing techniques. - Abstract: Load frequency control (LFC) plays a very important role in providing quality power both in the case of isolated as well as interconnected power systems. In order to maintain good quality power supply, the LFC should possess robustness toward the parametric uncertainty of the system and good disturbance rejection capability. The fractional order controller has the properties such as, eliminating steady state error, robustness toward plant gain variations and also good disturbance rejection. This makes the fractional order PID (FOPID) controller quite suitable for the LFC. Therefore, in this paper a FOPID is designed for single area LFC for all three types of turbines i.e., non-reheated, reheated and hydro turbines. It is observed that the FOPID controller shows better robustness toward ±50% parametric uncertainty and disturbance rejection capability than the existing techniques. Finally, the optimization of controller parameters and robustness evaluation of the control technique is done on the basis of the integral error criterion

17. Integrable coupling system of fractional soliton equation hierarchy

Energy Technology Data Exchange (ETDEWEB)

Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2009-10-05

In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.

18. Spiking and bursting patterns of fractional-order Izhikevich model

Science.gov (United States)

Teka, Wondimu W.; Upadhyay, Ranjit Kumar; Mondal, Argha

2018-03-01

Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.

19. SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES

Directory of Open Access Journals (Sweden)

S.ZIBAEI

2016-12-01

Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.

20. Atmospheric Turbulence Modeling for Aerospace Vehicles: Fractional Order Fit

Science.gov (United States)

Kopasakis, George (Inventor)

2015-01-01

An improved model for simulating atmospheric disturbances is disclosed. A scale Kolmogorov spectral may be scaled to convert the Kolmogorov spectral into a finite energy von Karman spectral and a fractional order pole-zero transfer function (TF) may be derived from the von Karman spectral. Fractional order atmospheric turbulence may be approximated with an integer order pole-zero TF fit, and the approximation may be stored in memory.

1. An extended integrable fractional-order KP soliton hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2011-01-17

In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.

2. Robust fractional order differentiators using generalized modulating functions method

KAUST Repository

Liu, Dayan

2015-02-01

This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

3. Fractional order differential inclusions on the half-line

Directory of Open Access Journals (Sweden)

Mouffak Benchohra

2010-06-01

Full Text Available We are concerned with the existence of bounded solutions of a boundary value problem on an unbounded domain for fractional order differential inclusions involving the Caputo fractional derivative. Our results are based on the fixed point theorem of Bohnnenblust-Karlin combined with the diagonalization method.

4. Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

Directory of Open Access Journals (Sweden)

Lakshman Mahto

2013-01-01

Full Text Available We use Sadovskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.

5. A new operational matrix of fractional order integration for the ...

49

M. H. Heydari1, M. R. Hooshmandasl2, C. Cattani3. 1,2Faculty of ... (CWs) together with spectral Galerkin method is proposed for solving a class of nonlinear multi-order fractional differential equations .... with their operational matrix of fractional integration is proposed for solving the following NMFDE: Dα. ∗ u(x) + s. ∑ i=1.

6. Theory of fractional order elements based impedance matching networks

KAUST Repository

2011-03-01

Fractional order circuit elements (inductors and capacitors) based impedance matching networks are introduced for the first time. In comparison to the conventional integer based L-type matching networks, fractional matching networks are much simpler and versatile. Any complex load can be matched utilizing a single series fractional element, which generally requires two elements for matching in the conventional approach. It is shown that all the Smith chart circles (resistance and reactance) are actually pairs of completely identical circles. They appear to be single for the conventional integer order case, where the identical circles completely overlap each other. The concept is supported by design equations and impedance matching examples. © 2010 IEEE.

7. Wavelet Methods for Solving Fractional Order Differential Equations

Directory of Open Access Journals (Sweden)

A. K. Gupta

2014-01-01

Full Text Available Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linear and nonlinear fractional differential equations. Our goal is to analyze the selected wavelet methods and assess their accuracy and efficiency with regard to solving fractional differential equations. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on various wavelets in order to solve differential equations of arbitrary order.

8. An approach to design controllers for MIMO fractional-order plants based on parameter optimization algorithm.

Science.gov (United States)

Xue, Dingyü; Li, Tingxue

2017-04-27

The parameter optimization method for multivariable systems is extended to the controller design problems for multiple input multiple output (MIMO) square fractional-order plants. The algorithm can be applied to search for the optimal parameters of integer-order controllers for fractional-order plants with or without time delays. Two examples are given to present the controller design procedures for MIMO fractional-order systems. Simulation studies show that the integer-order controllers designed are robust to plant gain variations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

9. Design and analysis of fractional order seismic transducer for displacement and acceleration measurements

Science.gov (United States)

Veeraian, Parthasarathi; Gandhi, Uma; Mangalanathan, Umapathy

2018-04-01

Seismic transducers are widely used for measurement of displacement, velocity, and acceleration. This paper presents the design of seismic transducer in the fractional domain for the measurement of displacement and acceleration. The fractional order transfer function for seismic displacement and acceleration transducer are derived using Grünwald-Letnikov derivative. Frequency response analysis of fractional order seismic displacement transducer (FOSDT) and fractional order seismic acceleration transducer (FOSAT) are carried out for different damping ratio with the different fractional order, and the maximum dynamic measurement range is identified. The results demonstrate that fractional order seismic transducer has increased dynamic measurement range and less phase distortion as compared to the conventional seismic transducer even with a lower damping ratio. Time response of FOSDT and FOSAT are derived analytically in terms of Mittag-Leffler function, the effect of fractional behavior in the time domain is evaluated from the impulse and step response. The fractional order system is found to have significantly reduced overshoot as compared to the conventional transducer. The fractional order seismic transducer design proposed in this paper is illustrated with a design example for FOSDT and FOSAT. Finally, an electrical equivalent of FOSDT and FOSAT is considered, and its frequency response is found to be in close agreement with the proposed fractional order seismic transducer.

10. Hipergeometric solutions to some nonhomogeneous equations of fractional order

Science.gov (United States)

Olivares, Jorge; Martin, Pablo; Maass, Fernando

2017-12-01

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 functions.

11. Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Jing Wu

2012-01-01

Full Text Available We study the eigenvalue interval for the existence of positive solutions to a semipositone higher order fractional differential equation = =   where ,  , , , satisfying , is the standard Riemann-Liouville derivative, , and is allowed to be changing-sign. By using reducing order method, the eigenvalue interval of existence for positive solutions is obtained.

12. A new operational matrix of fractional order integration for the ...

M H HEYDARI

2018-04-24

Apr 24, 2018 ... By using the CWs and their operational matrix of fractional order integration and Galerkin method, the ... tional order integration for the Haar wavelets [36], Legendre wavelets [23–25,29,30,47] and the ... the resulting approximation is continuous and can not properly model the discontinuities. In remote ...

13. Experimental demonstration of fractional-order oscillators of orders 2.6 and 2.7

KAUST Repository

Elwakil, A.S.

2017-02-07

The purpose of this work is to provide an experimental demonstration for the development of sinusoidal oscillations in a fractional-order Hartley-like oscillator. Solid-state fractional-order electric double-layer capacitors were first fabricated using graphene-percolated P(VDF-TrFE-CFE) composite structure, and then characterized by using electrochemical impedance spectroscopy. The devices exhibit the fractional orders of 0.6 and 0.74 respectively (using the model Zc=Rs+1/(jω)αCα), with the corresponding pseudocapacitances of approximately 93nFsec−0.4 and 1.5nFsec−0.26 over the frequency range 200kHz–6MHz (Rs < 15Ω). Then, we verified using these fractional-order devices integrated in a Hartley-like circuit that the fractional-order oscillatory behaviors are of orders 2.6 and 2.74.

14. A fractional-order model for MINMOD Millennium.

Science.gov (United States)

Cho, Yongjin; Kim, Imbunm; Sheen, Dongwoo

2015-04-01

MINMOD Millennium has been widely used to estimate insulin sensitivity (SI) in glucose-insulin dynamics. In order to explain the rheological behavior of glucose-insulin we attempt to modify MINMOD Millennium with fractional-order differentiation of order α ∈ (0, 1]. We show that the new modified model has non-negative, bounded solutions and a stable equilibrium point. Quasi-optimal fractional orders and parameters are estimated by using a nonlinear weighted least-squares method, the Levenberg-Marquardt algorithm, and the fractional Adams-Bashforth-Moulton method for several subjects (normal subjects and type 2 diabetic patients). The numerical results confirm that SI is significantly lower in diabetics than in non-diabetics. In addition, we explain the new factor (τ(1 - α)) determining glucose tolerance and the relation between SI and τ(1 - α). Copyright © 2015 Elsevier Inc. All rights reserved.

15. Measuring memory with the order of fractional derivative

Science.gov (United States)

Du, Maolin; Wang, Zaihua; Hu, Haiyan

2013-12-01

Fractional derivative has a history as long as that of classical calculus, but it is much less popular than it should be. What is the physical meaning of fractional derivative? This is still an open problem. In modeling various memory phenomena, we observe that a memory process usually consists of two stages. One is short with permanent retention, and the other is governed by a simple model of fractional derivative. With the numerical least square method, we show that the fractional model perfectly fits the test data of memory phenomena in different disciplines, not only in mechanics, but also in biology and psychology. Based on this model, we find that a physical meaning of the fractional order is an index of memory.

16. Novel Fractional Order Calculus Extended PN for Maneuvering Targets

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Jikun Ye

2017-01-01

Full Text Available Based on the theory of fractional order calculus (FOC, a novel extended proportional guidance (EPN law for intercepting the maneuvering target is proposed. In the first part, considering the memory function and filter characteristic of FOC, the novel extended PN guidance algorithm is developed based on the conventional PN after introducing the properties and operation rules of FOC. Further, with the help of FOC theory, the average load and ballistics characteristics of proposed guidance law are analyzed. Then, using the small offset kinematic model, the robustness of the new guidance law against autopilot parameters is studied theoretically by analyzing the sensitivity of the closed loop guidance system. At last, representative numerical results show that the designed guidance law obtains a better performance than the traditional PN for maneuvering target.

17. Dynamical analysis of fractional order model of immunogenic tumors

Directory of Open Access Journals (Sweden)

2016-07-01

Full Text Available In this article, we examine the fractional order model of the cytotoxic T lymphocyte response to a growing tumor cell population. We investigate the long-term behavior of tumor growth and explore the conditions of tumor elimination analytically. We establish the conditions for the tumor-free equilibrium and tumor-infection equilibrium to be asymptotically stable and provide the expression of the basic reproduction number. Existence of physical significant tumor-infection equilibrium points is investigated analytically. We show that tumor growth rate, source rate of immune cells, and death rate of immune cells play vital role in tumor dynamics and system undergoes saddle-node and transcritical bifurcation based on these parameters. Furthermore, the effect of cancer treatment is discussed by varying the values of relevant parameters. Numerical simulations are presented to illustrate the analytical results.

18. An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

Directory of Open Access Journals (Sweden)

Ricardo Almeida

2013-01-01

Full Text Available We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.

19. An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

Science.gov (United States)

Almeida, Ricardo

2013-01-01

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type. PMID:24319382

20. Tensor Fields for Use in Fractional-Order Viscoelasticity

Science.gov (United States)

Freed, Alan D.; Diethelm, Kai

2003-01-01

To be able to construct viscoelastic material models from fractional0order differentegral equations that are applicable for 3D finite-strain analysis requires definitions for fractional derivatives and integrals for symmetric tensor fields, like stress and strain. We define these fields in the body manifold. We then map them ito spatial fields expressed in terms of an Eulerian or Lagrangian reference frame where most analysts prefer to solve boundary problems.

1. Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment

KAUST Repository

Liu, Dayan

2015-03-31

The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann-Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters\\' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann-Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises.

2. Lyapunov-type inequalities for a higher order fractional differential equation with fractional integral boundary conditions

Directory of Open Access Journals (Sweden)

Mohamed Jleli

2017-03-01

where $n\\in \\mathbb N$, $n\\geq 2$, $n-1<\\alphafractional derivative of order$\\alpha$,$I_a^{\\alpha}$denotes the Riemann--Liouville fractional integral of order$\\alpha$, and$q,h\\in C([a,b];\\mathbb R$. As an application, we obtain numerical approximations of lower bound for the eigenvalues of corresponding equations. 3. (N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations Science.gov (United States) Arshad, Muhammad; Lu, Dianchen; Wang, Jun 2017-07-01 In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software. 4. Study on the Business Cycle Model with Fractional-Order Time Delay under Random Excitation Directory of Open Access Journals (Sweden) Zifei Lin 2017-07-01 Full Text Available Time delay of economic policy and memory property in a real economy system is omnipresent and inevitable. In this paper, a business cycle model with fractional-order time delay which describes the delay and memory property of economic control is investigated. Stochastic averaging method is applied to obtain the approximate analytical solution. Numerical simulations are done to verify the method. The effects of the fractional order, time delay, economic control and random excitation on the amplitude of the economy system are investigated. The results show that time delay, fractional order and intensity of random excitation can all magnify the amplitude and increase the volatility of the economy system. 5. Put order picking system Directory of Open Access Journals (Sweden) Đurđević Dragan D. 2014-01-01 Full Text Available Nowadays the warehouse is very important logistic component of the supply chain, where order-picking systems have important role. Due to the significant impact on logistics performance permanent goals are to increase efficiency and reduce the cost of these systems. To achieve these goals, there are different researches, and their success is determined by the achieved performances. Performances order picking process are dependent on the applied technology concepts of order-picking system, as well as the ways in which it is organized and managed. In addition to the standard conceptions (the man to good and good to the man is one of the newer, so-called. 'put' system - the inverse order-picking. The aim of this paper is to describe this concept, point out its core strengths and weaknesses and provide a basis that may be of importance in the development of warehouse technological solutions and application of this order-picking systems concept. 6. Approximation of Analytic Functions by Bessel's Functions of Fractional Order Directory of Open Access Journals (Sweden) Soon-Mo Jung 2011-01-01 Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order. 7. Stability analysis of fractional-order Hopfield neural networks with time delays. Science.gov (United States) Wang, Hu; Yu, Yongguang; Wen, Guoguang 2014-07-01 This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper. Copyright © 2014 Elsevier Ltd. All rights reserved. 8. Intelligent fractions learning system: implementation CSIR Research Space (South Africa) Smith, Andrew C 2011-05-01 Full Text Available to capture and analyse the children?s interactions), the scalability of the system makes it attractive in applications where automatic data capture is required. This paper is structured as follows. First, we describe the objectives of the system. Next we... to fractions. Our aim with the current research project is to extend the existing UFractions learning system to incorporate automatic data capturing. ?Intelligent UFractions? allows a teacher to remotely monitor the children?s progress during... 9. Existence results for higher order fractional differential inclusions with multi-strip fractional integral boundary conditions Directory of Open Access Journals (Sweden) Bashir Ahmad 2013-03-01 Full Text Available This paper investigates the existence of solutions for higher order fractional differential inclusions with fractional integral boundary conditions involving nonintersecting finite many strips of arbitrary length. Our study includes the cases when the right-hand side of the inclusion has convex as well non-convex values. Some standard fixed point theorems for multivalued maps are applied to establish the main results. An illustrative example is also presented. 10. Fractional-Order Control of a Micrometric Linear Axis Directory of Open Access Journals (Sweden) Luca Bruzzone 2013-01-01 Full Text Available This paper discusses the application of a particular fractional-order control scheme, the PDD1/2, to the position control of a micrometric linear axis. The PDD1/2 scheme derives from the classical PD scheme with the introduction of the half-derivative term. The PD and PDD1/2 schemes are compared by adopting a nondimensional approach for the sake of generality. The linear model of the closed-loop system is discussed by analysing the pole location in the σ-plane. Then, different combinations of the derivative and half-derivative terms, characterized by the same settling energy in the step response, are experimentally compared in the real mechatronic application, with nonnegligible friction effects and a position set point with trapezoidal speed law. The experimental results are coherent with the nonlinear model of the controlled system and confirm that the introduction of the half-derivative term is an interesting option for reducing the tracking error in the transient state. 11. Fractional Low-Order Joint Moments in the Estimation of Fractional Motions Science.gov (United States) Carsteanu, Alin Andrei; Guzman Sanluis, Javier Allan; Delvia Borjas López, Ada 2017-04-01 Fractional motions arise naturally from the integration of fractional noises, signals that appear in a variety of geophysical processes. When the marginal limiting probability distributions of these processes are Gaussian, the scaling behaviour of integer moments, be they marginal or joint - such as linear autocorrelation - can be used to parameterize the process. When, however, those moments do not converge, due to the heavy tails of the distributions, fractional low-order moments offer an attractive alternative. An application thereof to hydrometeorological data is presented herein. 12. Stability and synchronization of memristor-based fractional-order delayed neural networks. Science.gov (United States) Chen, Liping; Wu, Ranchao; Cao, Jinde; Liu, Jia-Bao 2015-11-01 Global asymptotic stability and synchronization of a class of fractional-order memristor-based delayed neural networks are investigated. For such problems in integer-order systems, Lyapunov-Krasovskii functional is usually constructed, whereas similar method has not been well developed for fractional-order nonlinear delayed systems. By employing a comparison theorem for a class of fractional-order linear systems with time delay, sufficient condition for global asymptotic stability of fractional memristor-based delayed neural networks is derived. Then, based on linear error feedback control, the synchronization criterion for such neural networks is also presented. Numerical simulations are given to demonstrate the effectiveness of the theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved. 13. Two-degree-of-freedom fractional order-PID controllers design for fractional order processes with dead-time. Science.gov (United States) Li, Mingjie; Zhou, Ping; Zhao, Zhicheng; Zhang, Jinggang 2016-03-01 Recently, fractional order (FO) processes with dead-time have attracted more and more attention of many researchers in control field, but FO-PID controllers design techniques available for the FO processes with dead-time suffer from lack of direct systematic approaches. In this paper, a simple design and parameters tuning approach of two-degree-of-freedom (2-DOF) FO-PID controller based on internal model control (IMC) is proposed for FO processes with dead-time, conventional one-degree-of-freedom control exhibited the shortcoming of coupling of robustness and dynamic response performance. 2-DOF control can overcome the above weakness which means it realizes decoupling of robustness and dynamic performance from each other. The adjustable parameter η2 of FO-PID controller is directly related to the robustness of closed-loop system, and the analytical expression is given between the maximum sensitivity specification Ms and parameters η2. In addition, according to the dynamic performance requirement of the practical system, the parameters η1 can also be selected easily. By approximating the dead-time term of the process model with the first-order Padé or Taylor series, the expressions for 2-DOF FO-PID controller parameters are derived for three classes of FO processes with dead-time. Moreover, compared with other methods, the proposed method is simple and easy to implement. Finally, the simulation results are given to illustrate the effectiveness of this method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved. 14. Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits Science.gov (United States) Kopasakis, George 2015-01-01 Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest. 15. Mutual transformations of fractional-order and integer-order optical vortices Science.gov (United States) Alexeyev, C. N.; Egorov, Yu. A.; Volyar, A. V. 2017-12-01 In this paper we studied the shaping and evolution of singular beams bearing optical vortices with fractional topological charges both in uniform and nonuniform anisotropic media. Starting from representation of the fractional-order vortex states as a superposition of an infinite number of integer-order vortices with certain energy distributions (the vortex spectra) we showed that the smooth wave front of the fractional vortex beam can either decay into an asymmetric array of integer-order vortices or, vice versa, the array of optical vortices can form a smooth helicoid-shaped wave front. We showed that by superimposing a finite number of the fractional-order vortex beams one can shape symmetric singular beams with arbitrary valued topological charges. We demonstrated that in biaxial crystals under the condition of the conical diffraction the fractional-order vortices are unstable. We also demonstrated that the circular fiber array with a space-variant birefringence is an appropriate medium for fractional-order vortex beams. In such arrays the supermodes may bear the half-integer-order vortices in circular components. Forming such supermodes plays a decisive role in evanescent-coupling assisted phase locking of individual fiber modes combined with tunneling of polarization states between anisotropic fibers in the array. We showed that the integer-charge phase increment in a fractional-order supermode consists of two half-integer-charge phase contributions. The explicit phase contribution is connected with the Pancharatnam-Berry phase that arises due to the phenomenon of nonadiabatic following. The implicit half-integer-charge phase contribution (or the "hidden phase") happens due to the sign alteration of the amplitude factors in the field components that corresponds to the wave-front cuts. We have also made the comparison of the hidden and hydrodynamic phases in superfluidic fractional-charge vortices with analogous phases in fractional-order supermodes. We have 16. Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time. Science.gov (United States) Das, Saptarshi; Pan, Indranil; Das, Shantanu 2013-07-01 Fuzzy logic based PID controllers have been studied in this paper, considering several combinations of hybrid controllers by grouping the proportional, integral and derivative actions with fuzzy inferencing in different forms. Fractional order (FO) rate of error signal and FO integral of control signal have been used in the design of a family of decomposed hybrid FO fuzzy PID controllers. The input and output scaling factors (SF) along with the integro-differential operators are tuned with real coded genetic algorithm (GA) to produce optimum closed loop performance by simultaneous consideration of the control loop error index and the control signal. Three different classes of fractional order oscillatory processes with various levels of relative dominance between time constant and time delay have been used to test the comparative merits of the proposed family of hybrid fractional order fuzzy PID controllers. Performance comparison of the different FO fuzzy PID controller structures has been done in terms of optimal set-point tracking, load disturbance rejection and minimal variation of manipulated variable or smaller actuator requirement etc. In addition, multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to study the Pareto optimal trade-offs between the set point tracking and control signal, and the set point tracking and load disturbance performance for each of the controller structure to handle the three different types of processes. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved. 17. A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives Directory of Open Access Journals (Sweden) Duan Jun-Sheng 2017-12-01 Full Text Available We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order α of the fractional derivative and the parameter γ parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter γ, not exactly like the case of single fractional-order derivative for the order α. The case of the distributed-order derivative provides us more options for the weight function and parameters. 18. Robust stability of fractional order polynomials with complicated uncertainty structure. Science.gov (United States) Matušů, Radek; Şenol, Bilal; Pekař, Libor 2017-01-01 The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. 19. Fractional order PID controller for improvement of PMSM speed control in aerospace applications Energy Technology Data Exchange (ETDEWEB) Saraji, Ali Motalebi [Young Researchers and Elite Club, AliAbad Katoul Branch, Islamic Azad University, AliAbad Katoul (Iran, Islamic Republic of); Ghanbari, Mahmood [Department of Electrical Engineering, AliAbad Katoul Branch, Islamic Azad University, AliAbad Katoul (Iran, Islamic Republic of) 2014-12-10 Because of the benefits reduced size, cost and maintenance, noise, CO2 emissions and increased control flexibility and precision, to meet these expectations, electrical equipment increasingly utilize in modern aircraft systems and aerospace industry rather than conventional mechanic, hydraulic, and pneumatic power systems. Electric motor drives are capable of converting electrical power to drive actuators, pumps, compressors, and other subsystems at variable speeds. In the past decades, permanent magnet synchronous motor (PMSM) and brushless dc (BLDC) motor were investigated for aerospace applications such as aircraft actuators. In this paper, the fractional-order PID controller is used in the design of speed loop of PMSM speed control system. Having more parameters for tuning fractional order PID controller lead to good performance ratio to integer order. This good performance is shown by comparison fractional order PID controller with the conventional PI and tuned PID controller by Genetic algorithm in MATLAB soft wear. 20. Adaptative synchronization in multi-output fractional-order complex dynamical networks and secure communications Science.gov (United States) Mata-Machuca, Juan L.; Aguilar-López, Ricardo 2018-01-01 This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems. 1. Fractional-Order Identification and Control of Heating Processes with Non-Continuous Materials Directory of Open Access Journals (Sweden) Riccardo Caponetto 2016-11-01 Full Text Available The paper presents a fractional order model of a heating process and a comparison of fractional and standard PI controllers in its closed loop system. Preliminarily, an enhanced fractional order model for the heating process on non-continuous materials has been identified through a fitting algorithm on experimental data. Experimentation has been carried out on a finite length beam filled with three non-continuous materials (air, styrofoam, metal buckshots in order to identify a model in the frequency domain and to obtain a relationship between the fractional order of the heating process and the different materials’ properties. A comparison between the experimental model and the theoretical one has been performed, proving a significant enhancement of the fitting performances. Moreover the obtained modelling results confirm the fractional nature of the heating processes when diffusion occurs in non-continuous composite materials, and they show how the model’s fractional order can be used as a characteristic parameter for non-continuous materials with different composition and structure. Finally, three different kinds of controllers have been applied and compared in order to keep constant the beam temperature constant at a fixed length. 2. Wiener-Hopf optimal control of a hydraulic canal prototype with fractional order dynamics. Science.gov (United States) Feliu-Batlle, Vicente; Feliu-Talegón, Daniel; San-Millan, Andres; Rivas-Pérez, Raúl 2017-06-26 This article addresses the control of a laboratory hydraulic canal prototype that has fractional order dynamics and a time delay. Controlling this prototype is relevant since its dynamics closely resembles the dynamics of real main irrigation canals. Moreover, the dynamics of hydraulic canals vary largely when the operation regime changes since they are strongly nonlinear systems. All this makes difficult to design adequate controllers. The controller proposed in this article looks for a good time response to step commands. The design criterium for this controller is minimizing the integral performance index ISE. Then a new methodology to control fractional order processes with a time delay, based on the Wiener-Hopf control and the Padé approximation of the time delay, is developed. Moreover, in order to improve the robustness of the control system, a gain scheduling fractional order controller is proposed. Experiments show the adequate performance of the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved. 3. Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation Science.gov (United States) Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun 2016-08-01 In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system. 4. Quantum Entanglement and the Topological Order of Fractional Hall States Science.gov (United States) Rezayi, Edward 2015-03-01 Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140. 5. Tunable fractional-order capacitor using layered ferroelectric polymers KAUST Repository Agambayev, Agamyrat 2017-09-05 Pairs of various Polyvinylidene fluoride P(VDF)-based polymers are used for fabricating bilayer fractional order capacitors (FOCs). The polymer layers are constructed using a simple drop casting approach. The resulting FOC has two advantages: It can be easily integrated with printed circuit boards, and its constant phase angle (CPA) can be tuned by changing the thickness ratio of the layers. Indeed, our experiments show that the CPA of the fabricated FOCs can be tuned within the range from -83° to -65° in the frequency band changing from 150 kHz to 10 MHz. Additionally, we provide an empirical formula describing the relationship between the thickness ratio and the CPA, which is highly useful for designing FOCs with the desired CPA. 6. Fractional-order positive position feedback compensator for active vibration control of a smart composite plate Science.gov (United States) Marinangeli, L.; Alijani, F.; HosseinNia, S. Hassan 2018-01-01 In this paper, Active Vibration Control (AVC) of a rectangular carbon fibre composite plate with free edges is presented. The plate is subjected to out-of-plane excitation by a modal vibration exciter and controlled by Macro Fibre Composite (MFC) transducers. Vibration measurements are performed by using a Laser Doppler Vibrometer (LDV) system. A fractional-order Positive Position Feedback (PPF) compensator is proposed, implemented and compared to the standard integer-order PPF. MFC actuator and sensor are positioned on the plate based on maximal modal strain criterion, so as to control the second natural mode of the plate. Both integer and fractional-order PPF allowed for the effective control of the second mode of vibration. However, the newly proposed fractional-order controller is found to be more efficient in achieving the same performance with less actuation voltage. Moreover, it shows promising performance in reducing spillover effect due to uncontrolled modes. 7. Fractional-order Viscoelasticity (FOV): Constitutive Development Using the Fractional Calculus: First Annual Report Science.gov (United States) Freed, Alan; Diethelm, Kai; Luchko, Yury 2002-01-01 This is the first annual report to the U.S. Army Medical Research and Material Command for the three year project "Advanced Soft Tissue Modeling for Telemedicine and Surgical Simulation" supported by grant No. DAMD17-01-1-0673 to The Cleveland Clinic Foundation, to which the NASA Glenn Research Center is a subcontractor through Space Act Agreement SAA 3-445. The objective of this report is to extend popular one-dimensional (1D) fractional-order viscoelastic (FOV) materials models into their three-dimensional (3D) equivalents for finitely deforming continua, and to provide numerical algorithms for their solution. 8. Distributed Coordination of Fractional Dynamical Systems with Exogenous Disturbances Directory of Open Access Journals (Sweden) Hongyong Yang 2014-01-01 Full Text Available Distributed coordination of fractional multiagent systems with external disturbances is studied. The state observer of fractional dynamical system is presented, and an adaptive pinning controller is designed for a little part of agents in multiagent systems without disturbances. This adaptive pinning controller with the state observer can ensure multiple agents' states reaching an expected reference tracking. Based on disturbance observers, the controllers are composited with the pinning controller and the state observer. By applying the stability theory of fractional order dynamical systems, the distributed coordination of fractional multiagent systems with external disturbances can be reached asymptotically. 9. New numerical approximation for solving fractional delay differential equations of variable order using artificial neural networks Science.gov (United States) Zúñiga-Aguilar, C. J.; Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Martínez, V. M.; Romero-Ugalde, H. M. 2018-02-01 In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated. 10. INTELLIGENT FRACTIONAL ORDER ITERATIVE LEARNING CONTROL USING FEEDBACK LINEARIZATION FOR A SINGLE-LINK ROBOT Directory of Open Access Journals (Sweden) Iman Ghasemi 2017-05-01 Full Text Available In this paper, iterative learning control (ILC is combined with an optimal fractional order derivative (BBO-Da-type ILC and optimal fractional and proportional-derivative (BBO-PDa-type ILC. In the update law of Arimoto's derivative iterative learning control, a first order derivative of tracking error signal is used. In the proposed method, fractional order derivative of the error signal is stated in term of 'sa' where to update iterative learning control law. Two types of fractional order iterative learning control namely PDa-type ILC and Da-type ILC are gained for different value of a. In order to improve the performance of closed-loop control system, coefficients of both and learning law i.e. proportional , derivative and are optimized using Biogeography-Based optimization algorithm (BBO. Outcome of the simulation results are compared with those of the conventional fractional order iterative learning control to verify effectiveness of BBO-Da-type ILC and BBO-PDa-type ILC 11. Synchronization of integral and fractional order chaotic systems a differential algebraic and differential geometric approach with selected applications in real-time CERN Document Server Martínez-Guerra, Rafael; Gómez-Cortés, Gian Carlo 2015-01-01 This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only... 12. On stability of fixed points and chaos in fractional systems Science.gov (United States) Edelman, Mark 2018-02-01 In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0 logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems. 13. Integro-differential equations of fractional order with nonlocal fractional boundary conditions associated with financial asset model Directory of Open Access Journals (Sweden) Bashir Ahmad 2013-02-01 Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented. 14. Impact of leakage delay on bifurcation in high-order fractional BAM neural networks. Science.gov (United States) Huang, Chengdai; Cao, Jinde 2018-02-01 The effects of leakage delay on the dynamics of neural networks with integer-order have lately been received considerable attention. It has been confirmed that fractional neural networks more appropriately uncover the dynamical properties of neural networks, but the results of fractional neural networks with leakage delay are relatively few. This paper primarily concentrates on the issue of bifurcation for high-order fractional bidirectional associative memory(BAM) neural networks involving leakage delay. The first attempt is made to tackle the stability and bifurcation of high-order fractional BAM neural networks with time delay in leakage terms in this paper. The conditions for the appearance of bifurcation for the proposed systems with leakage delay are firstly established by adopting time delay as a bifurcation parameter. Then, the bifurcation criteria of such system without leakage delay are successfully acquired. Comparative analysis wondrously detects that the stability performance of the proposed high-order fractional neural networks is critically weakened by leakage delay, they cannot be overlooked. Numerical examples are ultimately exhibited to attest the efficiency of the theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved. 15. On the formulation and numerical simulation of distributed-order fractional optimal control problems Science.gov (United States) Zaky, M. A.; Machado, J. A. Tenreiro 2017-11-01 In a fractional optimal control problem, the integer order derivative is replaced by a fractional order derivative. The fractional derivative embeds implicitly the time delays in an optimal control process. The order of the fractional derivative can be distributed over the unit interval, to capture delays of distinct sources. The purpose of this paper is twofold. Firstly, we derive the generalized necessary conditions for optimal control problems with dynamics described by ordinary distributed-order fractional differential equations (DFDEs). Secondly, we propose an efficient numerical scheme for solving an unconstrained convex distributed optimal control problem governed by the DFDE. We convert the problem under consideration into an optimal control problem governed by a system of DFDEs, using the pseudo-spectral method and the Jacobi-Gauss-Lobatto (J-G-L) integration formula. Next, we present the numerical solutions for a class of optimal control problems of systems governed by DFDEs. The convergence of the proposed method is graphically analyzed showing that the proposed scheme is a good tool for the simulation of distributed control problems governed by DFDEs. 16. Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative Directory of Open Access Journals (Sweden) Yongjun Shen 2014-01-01 Full Text Available The subharmonic resonance of van der Pol (VDP oscillator with fractional-order derivative is studied by the averaging method. At first, the first-order approximate solutions are obtained by the averaging method. Then the definitions of equivalent linear damping coefficient (ELDC and equivalent linear stiffness coefficient (ELSC for subharmonic resonance are established, and the effects of the fractional-order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed. Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established. The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR is also obtained. At last, the comparisons of the fractional-order and the traditional integer-order VDP oscillator are fulfilled by the numerical simulation. The effects of the parameters in fractional-order derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied. 17. Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay Directory of Open Access Journals (Sweden) Saïd Abbas 2013-01-01 Full Text Available In the present paper we investigate the existence of solutions for a system of integral inclusions of fractional order with multiple delay. Our results are obtained upon suitable fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler for the nonconvex case. 18. Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE OpenAIRE Sun, Chunlong; Li, Gongsheng; Jia, Xianzheng 2017-01-01 The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short) from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data... 19. Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β Directory of Open Access Journals (Sweden) Amal Khalaf Haydar 2016-01-01 Full Text Available The main aim in this paper is to use all the possible arrangements of objects such that r1 of them are equal to 1 and r2 (the others of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order 0<βfractional derivatives about the general fractional order n-1<βfractional initial value problems (FFIVPs are solved using the above two generalizations. 20. Blind third-order dispersion estimation based on fractional Fourier transformation for coherent optical communication Science.gov (United States) Yang, Lin; Guo, Peng; Yang, Aiying; Qiao, Yaojun 2018-02-01 In this paper, we propose a blind third-order dispersion estimation method based on fractional Fourier transformation (FrFT) in optical fiber communication system. By measuring the chromatic dispersion (CD) at different wavelengths, this method can estimation dispersion slope and further calculate the third-order dispersion. The simulation results demonstrate that the estimation error is less than 2 % in 28GBaud dual polarization quadrature phase-shift keying (DP-QPSK) and 28GBaud dual polarization 16 quadrature amplitude modulation (DP-16QAM) system. Through simulations, the proposed third-order dispersion estimation method is shown to be robust against nonlinear and amplified spontaneous emission (ASE) noise. In addition, to reduce the computational complexity, searching step with coarse and fine granularity is chosen to search optimal order of FrFT. The third-order dispersion estimation method based on FrFT can be used to monitor the third-order dispersion in optical fiber system. 1. Fractional order PIλDμ controller design for satisfying time and frequency domain specifications simultaneously. Science.gov (United States) Zheng, WeiJia; Luo, Ying; Wang, XiaoHong; Pi, YouGuo; Chen, YangQuan 2017-05-01 In order to achieve a desired control performance characterized by satisfying specifications in both frequency-domain and time-domain simultaneously, an optimal fractional order proportional integral derivative (PI λ D μ ) controller design strategy is proposed based on analytical calculation and Differential Evolution algorithm for a permanent magnet synchronous motor (PMSM) servo system in this paper. In this controller design, the frequency-domain specifications can guarantee the system stability with both gain margin and phase margin, and also the system robustness to loop gain variations. The time-domain specifications can ensure the desired step response performance with rapid rising curve, constrained overshoot, and proper power consuming. Compared with the PI λ controller and the traditional PID controller, PI λ D μ controller can get obvious benefits from two more degrees of freedom of the fractional orders λ and μ on satisfying multiple constraints simultaneously and achieving better servo tracking performance for the PMSM servo system. PMSM speed tracking simulations and experiments are demonstrated to show the significant advantages of using the proposed optimal PI λ D μ controller over the optimal fractional order PI λ controller and traditional integer order PID controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved. 2. Differential geometry of viscoelastic models with fractional-order derivatives International Nuclear Information System (INIS) Yajima, Takahiro; Nagahama, Hiroyuki 2010-01-01 Viscoelastic materials with memory effect are studied based on the fractional rheonomic geometry. The geometric objects are regarded as basic quantities of fractional viscoelastic models, i.e. the metric tensor and torsion tensor are interpreted as the strain and the fractional strain rate, respectively. The generalized viscoelastic equations are expressed by the geometric objects. Especially, the basic constitutive equations such as Voigt and Maxwell models can be derived geometrically from the generalized equation. This leads to the fact that various viscoelastic models can be unified into one geometric expression. 3. Fractional order models of viscoelasticity as an alternative in the analysis of red blood cell (RBC) membrane mechanics. Science.gov (United States) Craiem, Damian; Magin, Richard L 2010-01-20 New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress-strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues. 4. Fractional order models of viscoelasticity as an alternative in the analysis of red blood cell (RBC) membrane mechanics International Nuclear Information System (INIS) Craiem, Damian; Magin, Richard L 2010-01-01 New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress–strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues. (perspective) 5. Series Solutions of Time-Fractional Host-Parasitoid Systems Science.gov (United States) Arafa, A. A. M. 2011-12-01 In this paper, Adomian's decomposition method (ADM) has been used for solving time-fractional host-parasitoid system. The derivatives are understood in the Caputo sense. The reason of using fractional order differential equations (FOD) is that FOD are naturally related to systems with memory which exists in most biological systems. Also they are closely related to fractals which are abundant in biological systems. Numerical example justifies the proposed scheme. 6. Partially ordered algebraic systems CERN Document Server Fuchs, Laszlo 2011-01-01 Originally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap i 7. Application of Integer and Fractional Models in Electrochemical Systems Directory of Open Access Journals (Sweden) Isabel S. Jesus 2012-01-01 Full Text Available This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared. 8. Generalized Second-Order Parametric Optimality Conditions in Semiinfinite Discrete Minmax Fractional Programming and Second-Order Univexity Directory of Open Access Journals (Sweden) Ram Verma 2016-02-01 Full Text Available This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions. 9. Fractional Brownian motion of director fluctuations in nematic ordering DEFF Research Database (Denmark) Zhang, Z.; Mouritsen, Ole G.; Otnes, K. 1993-01-01 to determine the Hurst exponent H. Theory and experiment are in good agreement. A value of H congruent-to 1 was found for the nematic phase, characterizing fractional Brownian motion, whereas H congruent-to 0.5, reflecting ordinary Brownian motion, applies in the isotropic phase. Field-induced crossover from... 10. Pitchfork bifurcation and vibrational resonance in a fractional-order ... Indian Academy of Sciences (India) [18] J Sabatier, O P Agrawal and J A Tenreiro Machado, Advances in fractional calculus: Theoretical developments and applications in physics and engineering (Springer, Berlin,. 2007). [19] R Magin, Comput. Math. Appl. 59, 1586 (2010). [20] J T Machado, V Kiryakova and F Mainardi, Commun. Nonlinear Sci. Numer. 11. Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE Directory of Open Access Journals (Sweden) Chunlong Sun 2017-01-01 Full Text Available The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data give good approximations to the exact order demonstrating the efficiency of the inversion algorithm and numerical stability of the inversion problem. 12. Emotion recognition based on multiple order features using fractional Fourier transform Science.gov (United States) Ren, Bo; Liu, Deyin; Qi, Lin 2017-07-01 In order to deal with the insufficiency of recently algorithms based on Two Dimensions Fractional Fourier Transform (2D-FrFT), this paper proposes a multiple order features based method for emotion recognition. Most existing methods utilize the feature of single order or a couple of orders of 2D-FrFT. However, different orders of 2D-FrFT have different contributions on the feature extraction of emotion recognition. Combination of these features can enhance the performance of an emotion recognition system. The proposed approach obtains numerous features that extracted in different orders of 2D-FrFT in the directions of x-axis and y-axis, and uses the statistical magnitudes as the final feature vectors for recognition. The Support Vector Machine (SVM) is utilized for the classification and RML Emotion database and Cohn-Kanade (CK) database are used for the experiment. The experimental results demonstrate the effectiveness of the proposed method. 13. Using fractional order method to generalize strengthening generating operator buffer operator and weakening buffer operator OpenAIRE Wu, L.; Liu, S.; Yang, Yingjie 2016-01-01 Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases. 14. Nonlinear shallow water waves: A fractional order approach Directory of Open Access Journals (Sweden) Sarmad Arshad 2016-03-01 Full Text Available Nonlinear partial differential equations governing the obscure phenomena of shallow water waves are discussed in this article. Time fractional model is considered to understand the upcoming solutions on the basis of all historical states of the solution. A semi-analytic technique, Homotopy Perturbation Transform Method (HPTM is used in conjunction with a numerical technique to validate the approximate solutions. With the aid of graphical interpretation, the favorable wave parameters, to avoid wave breaking are estimated. 15. Initial value problem for a class of fractional order inhomogeneous equations in Banach spaces Science.gov (United States) Fedorov, Vladimir E.; Nazhimov, Roman R.; Gordievskikh, Dmitriy M. 2016-08-01 Initial value problem for a class of fractional order linear inhomogeneous equations in Banach spaces with a bounded operator at the unknown function is considered. The equation contains the Riemann-Liouville fractional derivative and the corresponding initial conditions are set for the fractional derivatives of a solution. The theorem of the problem unique solvability is proved. It is applied for studying of the solvability of initial boundary value problem for a filtration theory equation with Riemann-Liouville time-fractional order. 16. Numerical Solution for a Variable-Order Fractional Nonlinear Cable Equation via Chebyshev Cardinal Functions Science.gov (United States) Irandoust-Pakchin, Safar; Abdi-Mazraeh, Somayeh; Khani, Ali 2017-12-01 In this paper, a variable-order fractional derivative nonlinear cable equation is considered. It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of class of fractional partial differential equation with variable coefficient of fractional differential equation in various continues functions of spatial and time orders. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. Finally, illustrative examples are included to demonstrate the validity and applicability of the presented technique. 17. Bifurcation and chaos of a new discrete fractional-order logistic map Science.gov (United States) Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu 2018-04-01 The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps. 18. Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems Directory of Open Access Journals (Sweden) Junhai Luo 2014-01-01 Full Text Available This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order. 19. Dominant pole placement with fractional order PID controllers: D-decomposition approach. Science.gov (United States) Mandić, Petar D; Šekara, Tomislav B; Lazarević, Mihailo P; Bošković, Marko 2017-03-01 Dominant pole placement is a useful technique designed to deal with the problem of controlling a high order or time-delay systems with low order controller such as the PID controller. This paper tries to solve this problem by using D-decomposition method. Straightforward analytic procedure makes this method extremely powerful and easy to apply. This technique is applicable to a wide range of transfer functions: with or without time-delay, rational and non-rational ones, and those describing distributed parameter systems. In order to control as many different processes as possible, a fractional order PID controller is introduced, as a generalization of classical PID controller. As a consequence, it provides additional parameters for better adjusting system performances. The design method presented in this paper tunes the parameters of PID and fractional PID controller in order to obtain good load disturbance response with a constraint on the maximum sensitivity and sensitivity to noise measurement. Good set point response is also one of the design goals of this technique. Numerous examples taken from the process industry are given, and D-decomposition approach is compared with other PID optimization methods to show its effectiveness. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved. 20. Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks. Science.gov (United States) Chen, Boshan; Chen, Jiejie 2015-08-01 We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved. 1. Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop. Science.gov (United States) Tepljakov, Aleksei; Gonzalez, Emmanuel A; Petlenkov, Eduard; Belikov, Juri; Monje, Concepción A; Petráš, Ivo 2016-01-01 The problem of changing the dynamics of an existing DC motor control system without the need of making internal changes is considered in the paper. In particular, this paper presents a method for incorporating fractional-order dynamics in an existing DC motor control system with internal PI or PID controller, through the addition of an external controller into the system and by tapping its original input and output signals. Experimental results based on the control of a real test plant from MATLAB/Simulink environment are presented, indicating the validity of the proposed approach. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved. 2. Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order Science.gov (United States) Owolabi, Kolade M. 2017-03-01 In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed. 3. Measurement of fractional order model parameters of respiratory mechanical impedance in total liquid ventilation. Science.gov (United States) Beaulieu, Alexandre; Bossé, Dominick; Micheau, Philippe; Avoine, Olivier; Praud, Jean-Paul; Walti, Hervé 2012-02-01 This study presents a methodology for applying the forced-oscillation technique in total liquid ventilation. It mainly consists of applying sinusoidal volumetric excitation to the respiratory system, and determining the transfer function between the delivered flow rate and resulting airway pressure. The investigated frequency range was f ∈ [0.05, 4] Hz at a constant flow amplitude of 7.5 mL/s. The five parameters of a fractional order lung model, the existing "5-parameter constant-phase model," were identified based on measured impedance spectra. The identification method was validated in silico on computer-generated datasets and the overall process was validated in vitro on a simplified single-compartment mechanical lung model. In vivo data on ten newborn lambs suggested the appropriateness of a fractional-order compliance term to the mechanical impedance to describe the low-frequency behavior of the lung, but did not demonstrate the relevance of a fractional-order inertance term. Typical respiratory system frequency response is presented together with statistical data of the measured in vivo impedance model parameters. This information will be useful for both the design of a robust pressure controller for total liquid ventilators and the monitoring of the patient's respiratory parameters during total liquid ventilation treatment. © 2011 IEEE 4. Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat transfer problems Directory of Open Access Journals (Sweden) Yang Xiao-Jun 2017-01-01 Full Text Available In this paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer. 5. Symbolic representation for analog realization of a family of fractional order controller structures via continued fraction expansion. Science.gov (United States) Pakhira, Anindya; Das, Saptarshi; Pan, Indranil; Das, Shantanu 2015-07-01 This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative (FOPID) controller, FO[PD] controller and FO lead-lag compensator. Contemporary researchers have given several formulations for rational approximation of fractional order elements. However, approximation of the controllers studied in this paper, due to having fractional power of a rational transfer function, is not available in analog domain; although its digital realization already exists. This motivates us for applying CFE based analog realization technique for complicated FO controller structures to get equivalent rational transfer functions in terms of the controller tuning parameters. The symbolic expressions for rationalized transfer function in terms of the controller tuning parameters are especially important as ready references, without the need of running CFE algorithm every time and also helps in the synthesis of analog circuits for such FO controllers. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved. 6. Image fusion and denoising using fractional-order gradient information DEFF Research Database (Denmark) Mei, Jin-Jin; Dong, Yiqiu; Huang, Ting-Zhu Image fusion and denoising are signiﬁcant in image processing because of the availability of multi-sensor and the presence of the noise. The ﬁrst-order and second-order gradient information have been eﬀectively applied to deal with fusing the noiseless source images. In this paper, due....... By adding the data ﬁtting term between the fused image and a preprocessed image, a new convex variational model is proposed for fusing the noisy source images. Furthermore, an alternating direction method of multiplier (ADMM) is developed for solving the proposed variational model. Numerical experiments... 7. Fractional order of kinetics in LiF-TLD 100 International Nuclear Information System (INIS) Moharil, S.V. 1984-01-01 In a recent letter, it has been argued that the non-first-order kinetics for LiF-TLD 100 obtained by Kathuria and Sunta (J. Phys. D: Appl. Phys. 12, 1573) is an artefact of their experimental set-up. In this letter it is shown that this is not the case. (author) 8. Fractional-order integral and derivative controller for temperature ... Indian Academy of Sciences (India) For temperature control, it is usually recommended to use full. PID control, but with .... function of the output temperature change from the power input; thus, we use an approximated integer-order transfer ..... Tsai Ching-Chih, Lu Chi-Huang 1998 Multivariable self-tuning temperature control for plastic injec- tionmolding ... 9. A Digital Lego-Based Learning Environment for Fraction Ordering ... African Journals Online (AJOL) Learning environment is a process where learning is activated or enabled and the resources to support it are made available to a learner in order to construct and acquire knowledge. An environment must be simulated with features that enable learning to be fascinating, motivating and required mental process for critical ... 10. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order Directory of Open Access Journals (Sweden) Veyis Turut 2013-01-01 Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures. 11. Riemann-Christoffel Tensor in Differential Geometry of Fractional Order Application to Fractal Space-Time Science.gov (United States) Jumarie, Guy 2013-04-01 By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way. 12. Fractional diffusion equation with distributed-order material derivative. Stochastic foundations International Nuclear Information System (INIS) Magdziarz, M; Teuerle, M 2017-01-01 In this paper, we present the stochastic foundations of fractional dynamics driven by the fractional material derivative of distributed-order type. Before stating our main result, we present the stochastic scenario which underlies the dynamics given by the fractional material derivative. Then we introduce the Lévy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process. It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with the material derivative of distributed-order type. (paper) 13. Fractional Euler-Lagrange Equations Applied to Oscillatory Systems Directory of Open Access Journals (Sweden) Sergio Adriani David 2015-04-01 Full Text Available In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional nonlinear dynamic equations involving two classical physical applications: “Simple Pendulum” and the “Spring-Mass-Damper System” to both integer order calculus (IOC and fractional order calculus (FOC approaches. The numerical simulations were conducted and the time histories and pseudo-phase portraits presented. Both systems, the one that already had a damping behavior (Spring-Mass-Damper and the system that did not present any sort of damping behavior (Simple Pendulum, showed signs indicating a possible better capacity of attenuation of their respective oscillation amplitudes. This implication could mean that if the selection of the order of the derivative is conveniently made, systems that need greater intensities of damping or vibrating absorbers may benefit from using fractional order in dynamics and possibly in control of the aforementioned systems. Thereafter, we believe that the results described in this paper may offer greater insights into the complex behavior of these systems, and thus instigate more research efforts in this direction. 14. Controllability of fractional order integro-differential inclusions with infinite delay Directory of Open Access Journals (Sweden) Khalida Aissani 2014-11-01 Full Text Available This paper concerns for controllability of fractional order integro-differential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the controllability of fractional order integro-differential inclusions is obtained based on Dhage fixed point theorem. An example is given to illustrate the existence result. 15. Malatya Functions: Symmetric Functions Obtained by Applying Fractional Order Derivative to Karcı Entropy OpenAIRE Karci, Ali 2018-01-01 Shannonapplied derivative to a special probability function and obtained entropydefinition. Karcı converted the derivative with fractional order derivative andobtained a new definition for entropy. In this study, the fractional order ofderivative were selected as complex number and symmetric function wereobtained. Some of them were illustrated in this study, and it is known thatthere are infinite symmetric functions obtained by this way. 16. Fractional-Order Total Variation Image Restoration Based on Primal-Dual Algorithm OpenAIRE Dali Chen; YangQuan Chen; Dingyu Xue 2013-01-01 This paper proposes a fractional-order total variation image denoising algorithm based on the primal-dual method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, convergence rate, and blocky effect. The fractional-order total variation model is introduced by generalizing the first-order model, and the corresponding saddle-point and dual formulation are constructed in theory. In order to guarantee$O(1/{N}^{2})$conv... 17. Fractional-order integral and derivative controller for temperature ... Indian Academy of Sciences (India) moulding processes (http://www.manufacturing.net/ctl/article/CA408369.html) and Dihac et al (1992) used PID controller for a rapid thermal processor control. Lin et al (1999) pro- posed a neural fuzzy inference network for the temperature control of a water bath system and compared the performance with the PID control. 18. Pitchfork bifurcation and vibrational resonance in a fractional-order ... Indian Academy of Sciences (India) 2Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física,. Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain. 3Department of Mathematics and Computer Science, Huainan Normal University,. Huainan 232038, People's Republic of China. ∗. Corresponding author. 19. Designing an automated blood fractionation system. Science.gov (United States) McQuillan, Adrian C; Sales, Sean D 2008-04-01 UK Biobank will be collecting blood samples from a cohort of 500 000 volunteers and it is expected that the rate of collection will peak at approximately 3000 blood collection tubes per day. These samples need to be prepared for long-term storage. It is not considered practical to manually process this quantity of samples so an automated blood fractionation system is required. Principles of industrial automation were applied to the blood fractionation process leading to the requirement of developing a vision system to identify the blood fractions within the blood collection tube so that the fractions can be accurately aspirated and dispensed into micro-tubes. A prototype was manufactured and tested on a range of human blood samples collected in different tube types. A specially designed vision system was capable of accurately measuring the position of the plasma meniscus, plasma/buffy coat interface and the red cells/buffy coat interface within a vacutainer. A rack of 24 vacutainers could be processed in blood fractionation system offers a solution to the problem of processing human blood samples collected in vacutainers in a consistent manner and provides a means of ensuring data and sample integrity. 20. Comparison of the methods for discrete approximation of the fractional-order operator Directory of Open Access Journals (Sweden) Zborovjan Martin 2003-12-01 Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable. 1. Non-asymptotic fractional order differentiators via an algebraic parametric method KAUST Repository Liu, Dayan 2012-08-01 Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE. 2. Conformable fractional Dirac system on time scales Directory of Open Access Journals (Sweden) Tuba Gulsen 2017-07-01 Full Text Available Abstract We study the conformable fractional (CF Dirac system with separated boundary conditions on an arbitrary time scale T$\\mathbb{T}$. Then we extend some basic spectral properties of the classical Dirac system to the CF case. Eventually, some asymptotic estimates for the eigenfunction of the CF Dirac eigenvalue problem are obtained on T$\\mathbb{T} $. So, we provide a constructive procedure for the solution of this problem. These results are important steps to consolidate the link between fractional calculus and time scale calculus in spectral theory. 3. Analytical study of time-fractional order Klein–Gordon equation Directory of Open Access Journals (Sweden) Mohammad Tamsir 2016-03-01 Full Text Available In this article, we study an approximate analytical solution of linear and nonlinear time-fractional order Klein–Gordon equations by using a recently developed semi analytical method referred as fractional reduced differential transform method with appropriate initial condition. In the study of fractional Klein–Gordon equation, fractional derivative is described in the Caputo sense. The validity and efficiency of the aforesaid method are illustrated by considering three computational examples. The solution profile behavior and effects of different fraction Brownian motion on solution profile of the three numerical examples are shown graphically. 4. Isotopic fractionation of tritium in biological systems. Science.gov (United States) Le Goff, Pierre; Fromm, Michel; Vichot, Laurent; Badot, Pierre-Marie; Guétat, Philippe 2014-04-01 Isotopic fractionation of tritium is a highly relevant issue in radiation protection and requires certain radioecological considerations. Sound evaluation of this factor is indeed necessary to determine whether environmental compartments are enriched/depleted in tritium or if tritium is, on the contrary, isotopically well-distributed in a given system. The ubiquity of tritium and the standard analytical methods used to assay it may induce biases in both the measurement and the signification that is accorded to the so-called fractionation: based on an exhaustive review of the literature, we show how, sometimes large deviations may appear. It is shown that when comparing the non-exchangeable fraction of organically bound tritium (neOBT) to another fraction of tritium (e.g. tritiated water) the preparation of samples and the measurement of neOBT reported frequently led to underestimation of the ratio of tritium to hydrogen (T/H) in the non-exchangeable compartment by a factor of 5% to 50%. In the present study, corrections are proposed for most of the biological matrices studied so far. Nevertheless, the values of isotopic fractionation reported in the literature remain difficult to compare with each other, especially since the physical quantities and units often vary between authors. Some improvements are proposed to better define what should encompass the concepts of exchangeable and non-exchangeable fractions. Copyright © 2014 Elsevier Ltd. All rights reserved. 5. Nonlinear Fractional Sliding Mode Controller Based on Reduced Order FNPK Model for Output Power Control of Nuclear Research Reactors Science.gov (United States) Davijani, Nafiseh Zare; Jahanfarnia, Gholamreza; Abharian, Amir Esmaeili 2017-01-01 One of the most important issues with respect to nuclear reactors is power control. In this study, we designed a fractional-order sliding mode controller based on a nonlinear fractional-order model of the reactor system in order to track the reference power trajectory and overcome uncertainties and external disturbances. Since not all of the variables in an operating reactor are measurable or specified in the control law, we propose a reduced-order fractional neutron point kinetic (ROFNPK) model based on measurable variables. In the design, we assume the differences between the approximated model and the real system is limited. We use the obtained model in the controller design process and use the Lyapunov method to perform a stability analysis of the closed-loop system. We simulate the proposed reduced-order fractional-order sliding mode controller (ROFOSMC) using Matlab/Simulink, and its performance is compared with that of a reduced order integer-order sliding mode controller (ROIOSMC). Our simulation results indicate an acceptable performance of the proposed approach in tracking the reference power trajectory with respect to ROIOSMC because of faster response of control effort signal and the smaller tracking error. Moreover, the results illustrate the capability of the controller in rejection of the disturbance and the noise signals and the robustness of controller against uncertainty. 6. Improved Fractional Order VSS Inc-Cond MPPT Algorithm for Photovoltaic Scheme Directory of Open Access Journals (Sweden) R. Arulmurugan 2014-01-01 Full Text Available Nowadays a hot topic among the research community is the harnessing energy from the free sunlight which is abundant and pollution-free. The availability of cheap solar photovoltaic (PV modules has to harvest solar energy with better efficiency. The nature of solar modules is nonlinear and therefore the proper impedance matching is essential. The proper impedance matching ensures the extraction of the maximum power from solar PV module. Maximum power point tracking (MPPT algorithm is acting as a significant part in solar power generating system because it varies in the output power from a PV generating set for various climatic conditions. This paper suggested a new improved work for MPPT of PV energy system by using the optimized novel improved fractional order variable step size (FOVSS incremental conductance (Inc-Cond algorithm. The new proposed controller combines the merits of both improved fractional order (FO and variable step size (VSS Inc-Cond which is well suitable for design control and execution. The suggested controller results in attaining the desired transient reaction under changing operating points. MATLAB simulation effort shows MPPT controller and a DC to DC Luo converter feeding a battery load is achieved. The laboratory experimental results demonstrate that the new proposed MPPT controller in the photovoltaic generating system is valid. 7. Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings Directory of Open Access Journals (Sweden) Parinya Anantachaisilp 2017-01-01 Full Text Available One of the key issues in control design for Active Magnetic Bearing (AMB systems is the tradeoff between the simplicity of the controller structure and the performance of the closed-loop system. To achieve this tradeoff, this paper proposes the design of a fractional order Proportional-Integral-Derivative (FOPID controller. The FOPID controller consists of only two additional parameters in comparison with a conventional PID controller. The feasibility of FOPID for AMB systems is investigated for rotor suspension in both the radial and axial directions. Tuning methods are developed based on the evolutionary algorithms for searching the optimal values of the controller parameters. The resulting FOPID controllers are then tested and compared with a conventional PID controller, as well as with some advanced controllers such as Linear Quadratic Gausian (LQG and H ∞ controllers. The comparison is made in terms of various stability and robustness specifications, as well as the dimensions of the controllers as implemented. Lastly, to validate the proposed method, experimental testing is carried out on a single-stage centrifugal compressor test rig equipped with magnetic bearings. The results show that, with a proper selection of gains and fractional orders, the performance of the resulting FOPID is similar to those of the advanced controllers. 8. A Novel Sigma-Delta Modulator with Fractional-Order Digital Loop Integrator Directory of Open Access Journals (Sweden) Chi Xu 2017-01-01 Full Text Available This paper proposes using a fractional-order digital loop integrator to improve the robust stability of Sigma-Delta modulator, thus extending the integer-order Sigma-Delta modulator to a non-integer-order (fractional-order one in the Sigma-Delta ADC design field. The proposed fractional-order Sigma-Delta modulator has reasonable noise characteristics, dynamic range, and bandwidth; moreover the signal-to-noise ratio (SNR is improved remarkably. In particular, a 2nd-order digital loop integrator and a digital PIλDμ controller are combined to work as the fractional-order digital loop integrator, which is realized using FPGA; this will reduce the ASIC analog circuit layout design and chip testing difficulties. The parameters of the proposed fractional-order Sigma-Delta modulator are tuned by using swarm intelligent algorithm, which offers opportunity to simplify the process of tuning parameters and further improve the noise performance. Simulation results are given and they demonstrate the efficiency of the proposed fractional-order Sigma-Delta modulator. 9. reaction-diffusion system with fractional derivatives Directory of Open Access Journals (Sweden) Kamel Haouam 2006-01-01 Full Text Available We give some necessary conditions for local and global existence of a solution to reaction-diffusion system of type (FDS with temporal and spacial fractional derivatives. As in the case of single equation of type (STFE studied by M. Kirane et al. (2005, we prove that these conditions depend on the behavior of initial conditions for large |x|. 10. Transient Performance Iprovement of Wind Turbines with Doubly Fed Induction Generators Using Fractional Order Control Strategy Directory of Open Access Journals (Sweden) Samaneh Jenab 2014-01-01 Full Text Available Application of fractional order proportional integral (FOPI controller to improve transient performance of wind turbine (WT with Doubly fed induction generator (DFIG is presented and studied in this paper. By small signal analysis, it is found that the dynamic behavior of the DFIG based WT, during the variation of operating conditions, is strongly affected by the stator dynamics. Since the DFIG electrical dynamics are nonlinear, the linear control (PI scheme cannot work properly under change in wind speed and stator modes are not damped appropriately. The proposed fractional order controller generalizes the conventional integer order PI controller whose integral order are fractional number rather than integer. This expansion can provide more flexibility in achieving control objectives. By time domain simulations, a comparative analysis is made with respect to the standard PI controller to demonstrate effectiveness of the fractional order PI controller during wind speed perturbation. 11. An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation KAUST Repository Liu, Da-Yan 2015-04-30 This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator. 12. The Oscillation of a Class of the Fractional-Order Delay Differential Equations Directory of Open Access Journals (Sweden) Qianli Lu 2014-01-01 Full Text Available Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used. 13. Laser systems for ablative fractional resurfacing DEFF Research Database (Denmark) Paasch, Uwe; Haedersdal, Merete 2011-01-01 ablative laser systems. Fractionated CO(2) (10,600-nm), erbium yttrium aluminum garnet, 2940-nm and yttrium scandium gallium garnet, 2790-nm lasers are available. In this article, we present an overview of AFR technology, devices and histopathology, and we summarize the current clinical possibilities...... of a variety of skin conditions, primarily chronically photodamaged skin, but also acne and burn scars. In addition, it is anticipated that AFR can be utilized in the laser-assisted delivery of topical drugs. Clinical efficacy coupled with minimal downtime has driven the development of various fractional... 14. Fractional order differentiation and robust control design crone, h-infinity and motion control CERN Document Server Sabatier, Jocelyn; Melchior, Pierre; Oustaloup, Alain 2015-01-01 This monograph collates the past decade’s work on fractional models and fractional systems in the fields of analysis, robust control and path tracking. Themes such as PID control, robust path tracking design and motion control methodologies involving fractional differentiation are amongst those explored. It juxtaposes recent theoretical results at the forefront in the field, and applications that can be used as exercises that will help the reader to assimilate the proposed methodologies. The first part of the book deals with fractional derivative and fractional model definitions, as well as recent results for stability analysis, fractional model physical interpretation, controllability, and H-infinity norm computation. It also presents a critical point of view on model pseudo-state and “real state”, tackling the problem of fractional model initialization. Readers will find coverage of PID, Fractional PID and robust control in the second part of the book, which rounds off with an extension of H-infinity ... 15. Fractional-order PI based STATCOM and UPFC controller to diminish subsynchronous resonance. Science.gov (United States) Koteswara Raju, D; Umre, Bhimrao S; Junghare, Anjali S; Thakre, Mohan P; Motamarri, Rambabu; Somu, Chaitanya 2016-01-01 This research article proposes a powerful fractional-order PI controller to mitigate the subsynchronous oscillations in turbine-generator shaft due to subsynchronous resonance (SSR) with flexible AC transmission system devices such as static synchronous compensator (STATCOM) and unified power flow controller (UPFC). The diminution of SSR is achieved by the raising of network damping at those frequencies which are proximate to the torsional mode frequency of the turbine-generator shaft. The increase of network damping is obtained with the injection of subsynchronous frequency component of current and both current and voltage into the line. The subsynchronous component of current and voltage are derived from the measured signal of the system and further the same amount of shunt current is injected with STATCOM and simultaneous injection of current and voltage with UPFC into the transmission line to make the subsynchronous current to zero which is the prime source of turbine shaft oscillations. The insertion and proper tuning of Fractional-order PI controller in the control scheme, the subsynchronous oscillations are reduced to 92 % in case of STATCOM and 98 % in case of UPFC as compared to without controller and 14 % as compared with the results of conventional PI controller. The IEEE first benchmark model has adopted for analyze the effectiveness and speed of the proposed control scheme using MATLAB-Simulink and the corresponding results illustrates the precision and robustness of the proposed controller. 16. Laser systems for ablative fractional resurfacing DEFF Research Database (Denmark) Paasch, Uwe; Haedersdal, Merete 2011-01-01 ablative laser systems. Fractionated CO(2) (10,600-nm), erbium yttrium aluminum garnet, 2940-nm and yttrium scandium gallium garnet, 2790-nm lasers are available. In this article, we present an overview of AFR technology, devices and histopathology, and we summarize the current clinical possibilities...... with AFR incorporating our personal experience. AFR is still in the exploratory era, and systematic investigations of clinical outcomes related to various system settings are needed.... 17. A unified framework for testing in the linear regression model under unknown order of fractional integration DEFF Research Database (Denmark) Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional... 18. L1-Solutions of Boundary Value Problems for Implicit Fractional Order Differential Equations Directory of Open Access Journals (Sweden) Mouffak Benchohra 2015-12-01 Full Text Available The aim of this paper is to present new results on the existence of solutions for a class of boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. 19. Image Encryption Algorithm Based on a Novel Improper Fractional-Order Attractor and a Wavelet Function Map Directory of Open Access Journals (Sweden) Jian-feng Zhao 2017-01-01 Full Text Available This paper presents a three-dimensional autonomous chaotic system with high fraction dimension. It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. Based on the continuous chaos and the discrete wavelet function map, an image encryption algorithm is put forward. The key space is formed by the initial state variables, parameters, and orders of the system. Every pixel value is included in secret key, so as to improve antiattack capability of the algorithm. The obtained simulation results and extensive security analyses demonstrate the high level of security of the algorithm and show its robustness against various types of attacks. 20. Second order limit laws for occupation times of the fractional Brownian motion OpenAIRE Xu, Fangjun 2013-01-01 We prove second order limit laws for (additive) functionals of the$d$-dimensional fractional Brownian motion with Hurst index$H=\\frac{1}{d}$, using the method of moments, extending the Kallianpur-Robbins law. 1. Existence of three positive solutions for boundary value problem with fractional order and infinite delay Directory of Open Access Journals (Sweden) Benaouda Hedia 2015-07-01 Full Text Available In this paper we investigate the existence three positives solutions by using Leggett-Williams fixed point theorem in cones for three boundary value problem with fractional order and infinite delay. 2. Darboux problem for implicit impulsive partial hyperbolic fractional order differential equations Directory of Open Access Journals (Sweden) Said Abbas 2011-11-01 Full Text Available In this article we investigate the existence and uniqueness of solutions for the initial value problems, for a class of hyperbolic impulsive fractional order differential equations by using some fixed point theorems. 3. Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM Directory of Open Access Journals (Sweden) Firat Evirgen 2016-04-01 Full Text Available In this paper, a class of Nonlinear Programming problem is modeled with gradient based system of fractional order differential equations in Caputo's sense. To see the overlap between the equilibrium point of the fractional order dynamic system and theoptimal solution of the NLP problem in a longer timespan the Multistage Variational İteration Method isapplied. The comparisons among the multistage variational iteration method, the variationaliteration method and the fourth order Runge-Kutta method in fractional and integer order showthat fractional order model and techniques can be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programming problems. 4. Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law OpenAIRE Želi, Velibor; Zorica, Dušan 2017-01-01 Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through A... 5. 21 CFR 862.1630 - Protein (fractionation) test system. Science.gov (United States) 2010-04-01 ... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Protein (fractionation) test system. 862.1630... Systems § 862.1630 Protein (fractionation) test system. (a) Identification. A protein (fractionation) test system is a device intended to measure protein fractions in blood, urine, cerebrospinal fluid, and other... 6. Revisiting the approximate analytical solution of fractional-order gas dynamics equation Directory of Open Access Journals (Sweden) Mohammad Tamsir 2016-06-01 Full Text Available In this paper, an approximate analytical solution of the time fractional gas dynamics equation arising in the shock fronts, is obtained using a recent semi-analytical method referred as fractional reduced differential transform method. The fractional derivatives are considered in the Caputo sense. To validate the efficiency and reliability of the method, four numerical examples of the linear and nonlinear gas dynamics equations are considered. Computed results are compared with results available in the literature. It is found that obtained results agree excellently with DTM, and FHATM. The solutions behavior and its effects for different values of the fractional order are shown graphically. The main advantage of the method is easiness to implement and requires small size of computation. Hence, it is a very effective and efficient semi-analytical method for solving the fractional order gas dynamics equation. 7. Exotic Quantum Order in Low-Dimensional Systems OpenAIRE Girvin, Steven M. 1997-01-01 Strongly correlated quantum systems in low dimensions often exhibit novel quantum ordering. This ordering is sometimes hidden and can be revealed only by examining new dual' types of correlations. Such ordering leads to novel collective modes and fractional quantum numbers. Examples will be presented from quantum spin chains and the quantum Hall effect. 8. On Antiperiodic Boundary Value Problems for Higher-Order Fractional Differential Equations Directory of Open Access Journals (Sweden) Ahmed Alsaedi 2012-01-01 Full Text Available We study an antiperiodic boundary value problem of nonlinear fractional differential equations of order q∈(4,5]. Some existence results are obtained by applying some standard tools of fixed-point theory. We show that solutions for lower-order anti-periodic fractional boundary value problems follow from the solution of the problem at hand. Our results are new and generalize the existing results on anti-periodic fractional boundary value problems. The paper concludes with some illustrating examples. 9. Haze image enhancement based on space fractional-order partial differential equation Science.gov (United States) Xue, Wendan; Zhao, Fengqun 2017-07-01 Based on good amplitude frequency characteristics and the spatial global correlation of fractional-order differential, an energy functional of haze image enhancement is established by taking fractional derivative on both sides of the atmospheric physics scattering model, and a haze image enhancement model based on space fractional-order partial differential equation is obtained by using steepest descent method. Based on fast wavelet transform, the low-frequency part of patch transmission and the high-frequency part of point transmission are fused to estimate the transmission. Finally, the numerical solution of the fractional-order partial differential equation is obtained by the finite difference method. The experimental results show that the algorithm can improve the contrast, brightness and clarity of the image, and it is an effective image enhancement method for haze images. 10. Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay Science.gov (United States) Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia 2017-12-01 In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results. 11. The Fractional-Order mathematical modeling of bacterial resistance against multiple antibiotics in case of local bacterial infection Directory of Open Access Journals (Sweden) Bahatdin Daşbaşı 2017-06-01 Full Text Available In this study, it is described the general forms of fractional-order differential equations and asymtotic stability of their system’s equilibria. In addition that, the stability analysis of equilibrium points of the local bacterial infection model which is fractional-order differential equation system, is made. Results of this analysis are supported via numerical simulations drawn by datas obtained from literature for mycobacterium tuberculosis and the antibiotics isoniazid (INH, rifampicin (RIF, streptomycin (SRT and pyrazinamide (PRZ used against this bacterial infection. 12. Time fractional evolution of the two-level system interacting with light field Science.gov (United States) Lu, Longzhao; Yu, Xiangyang 2017-11-01 In this study, we construct a generalized time fractional Schrödinger equation. By applying this equation to the two-level system, the fractional optical Bloch model is developed. With the Mittage–Leffler function, the fractional equations of motion in the absence of light field are solved analytically. We propose the fractional resonance condition and verify it based on the interaction between the system and the monochromatic light. Then we calculate the fractional Rabi frequency with respect to the order of time derivative. Finally, we propose the concept of fractional recovery area and study the resonant interaction between the system and the optical pulse. 13. Mitigation of Subsynchronous Resonance with Fractional-order PI based UPFC controller Science.gov (United States) Raju, D. Koteswara; Umre, Bhimrao S.; Junghare, Anjali S.; Babu, B. Chitti 2017-02-01 Due to incorporation of series capacitor compensation in transmission line for stability improvement, subsynchronous oscillations are generated at turbine-generator shaft. These oscillations can damage the shaft system if these are not well suppressed. In order to damp out these oscillations, usually power system network should have sufficient damping and the increase of network damping is obtained by the injection of subsynchronous component of voltage and current into the line, which are extracted from the measured signal of the system. However, the effectiveness of damp out of these subsynchronous oscillations is possibly by incorporating UPFC in the transmission line network is of high interest and it should be further investigated. This research article proposes the mitigation of subsynchronous resonance (SSR) using fractional-order PI (FOPI) based unified power flow controller (UPFC). The robustness of the proposed controller is tested for 25%, 55% and 70% series compensation with a symmetrical fault (L-L-L fault). Further, Eigenvalue analysis and Fast Fourier Transform (FFT) analysis against operating point variations and uncertainties in the system are also examined. The IEEE first benchmark model is adopted for this study and the superiority of the FOPI based UPFC controller over PI based UPFC controller is discussed by comparing the results with various performance indices. 14. Performance Analysis of Fractional-Order PID Controller for a Parabolic Distributed Solar Collector KAUST Repository Elmetennani, Shahrazed 2017-09-01 This paper studies the performance of a fractional-order proportional integral derivative (FOPID) controller designed for parabolic distributed solar collectors. The control problem addressed in concentrated solar collectors aims at forcing the produced heat to follow a desired reference despite the unevenly varying solar irradiance. In addition to the unpredictable variations of the energy source, the parabolic solar collectors are subject to inhomogeneous distributed efficiency parameters affecting the heat production. The FOPID controller is well known for its simplicity with better tuning flexibility along with robustness with respect to disturbances. Thus, we propose a control strategy based on FOPID to achieve the control objectives. First, the FOPID controller is designed based on a linear approximate model describing the system dynamics under nominal working conditions. Then, the FOPID gains and differentiation orders are optimally tuned in order to fulfill the robustness design specifications by solving a nonlinear optimization problem. Numerical simulations are carried out to evaluate the performance of the proposed FOPID controller. A comparison to the robust integer order PID is also provided. Robustness tests are performed for the nominal model to show the effectiveness of the FOPID. Furthermore, the proposed FOPID is numerically tested to control the distributed solar collector under real working conditions. 15. Design of CMOS analog integrated fractional-order circuits applications in medicine and biology CERN Document Server Tsirimokou, Georgia; Elwakil, Ahmed 2017-01-01 This book describes the design and realization of analog fractional-order circuits, which are suitable for on-chip implementation, capable of low-voltage operation and electronic adjustment of their characteristics. The authors provide a brief introduction to fractional-order calculus, followed by design issues for fractional-order circuits of various orders and types. The benefits of this approach are demonstrated with current-mode and voltage-mode filter designs. Electronically tunable emulators of fractional-order capacitors and inductors are presented, where the behavior of the corresponding chips fabricated using the AMS 0.35um CMOS process has been experimentally verified. Applications of fractional-order circuits are demonstrated, including a pre-processing stage suitable for the implementation of the Pan-Tompkins algorithm for detecting the QRS complexes of an electrocardiogram (ECG), a fully tunable implementation of the Cole-Cole model used for the modeling of biological tissues, and a simple, non-i... 16. New Approaches to Minimum-Energy Design of Integer- and Fractional-Order Perfect Control Algorithms Science.gov (United States) Hunek, Wojciech P.; Wach, Łukasz 2017-10-01 In this paper the new methods concerning the energy-based minimization of the perfect control inputs is presented. For that reason the multivariable integer- and fractional-order models are applied which can be used for describing a various real world processes. Up to now, the classical approaches have been used in forms of minimum-norm/least squares inverses. Notwithstanding, the above-mentioned tool do not guarantee the optimal control corresponding to optimal input energy. Therefore the new class of inversebased methods has been introduced, in particular the new σ- and H-inverse of nonsquare parameter and polynomial matrices. Thus a proposed solution remarkably outperforms the typical ones in systems where the control runs can be understood in terms of different physical quantities, for example heat and mass transfer, electricity etc. A simulation study performed in Matlab/Simulink environment confirms the big potential of the new energy-based approaches. 17. Numerical solutions of multi-order fractional differential equations by Boubaker polynomials Directory of Open Access Journals (Sweden) Bolandtalat A. 2016-01-01 Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique. 18. Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions Directory of Open Access Journals (Sweden) Xin Liang 2018-01-01 Full Text Available In this paper, an anomalous advection-dispersion model involving a new general Liouville–Caputo fractional-order derivative is addressed for the first time. The series solutions of the general fractional advection-dispersion equations are obtained with the aid of the Laplace transform. The results are given to demonstrate the efficiency of the proposed formulations to describe the anomalous advection dispersion processes. 19. Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation Directory of Open Access Journals (Sweden) Wang Li 2017-06-01 Full Text Available In this paper, we study Lie symmetry analysis and conservation laws for the time fractional nonlinear fourth-order evolution equation. Using the method of Lie point symmetry, we provide the associated vector fields, and derive the similarity reductions of the equation, respectively. The method can be applied wisely and efficiently to get the reduced fractional ordinary differential equations based on the similarity reductions. Finally, by using the nonlinear self-adjointness method and Riemann-Liouville time-fractional derivative operator as well as Euler-Lagrange operator, the conservation laws of the equation are obtained. 20. ECG artifact cancellation in surface EMG signals by fractional order calculus application. Science.gov (United States) Miljković, Nadica; Popović, Nenad; Djordjević, Olivera; Konstantinović, Ljubica; Šekara, Tomislav B 2017-03-01 New aspects for automatic electrocardiography artifact removal from surface electromyography signals by application of fractional order calculus in combination with linear and nonlinear moving window filters are explored. Surface electromyography recordings of skeletal trunk muscles are commonly contaminated with spike shaped artifacts. This artifact originates from electrical heart activity, recorded by electrocardiography, commonly present in the surface electromyography signals recorded in heart proximity. For appropriate assessment of neuromuscular changes by means of surface electromyography, application of a proper filtering technique of electrocardiography artifact is crucial. A novel method for automatic artifact cancellation in surface electromyography signals by applying fractional order calculus and nonlinear median filter is introduced. The proposed method is compared with the linear moving average filter, with and without prior application of fractional order calculus. 3D graphs for assessment of window lengths of the filters, crest factors, root mean square differences, and fractional calculus orders (called WFC and WRC graphs) have been introduced. For an appropriate quantitative filtering evaluation, the synthetic electrocardiography signal and analogous semi-synthetic dataset have been generated. The examples of noise removal in 10 able-bodied subjects and in one patient with muscle dystrophy are presented for qualitative analysis. The crest factors, correlation coefficients, and root mean square differences of the recorded and semi-synthetic electromyography datasets showed that the most successful method was the median filter in combination with fractional order calculus of the order 0.9. Statistically more significant (p ECG peak reduction was obtained by the median filter application compared to the moving average filter in the cases of low level amplitude of muscle contraction compared to ECG spikes. The presented results suggest that the 1. A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation, and its optimal time domain tuning. Science.gov (United States) Kumar, Anupam; Kumar, Vijay 2017-05-01 In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved. 2. Demonstrative fractional order - PID controller based DC motor drive on digital platform. Science.gov (United States) Khubalkar, Swapnil W; Junghare, Anjali S; Aware, Mohan V; Chopade, Amit S; Das, Shantanu 2017-09-21 In industrial drives applications, fractional order controllers can exhibit phenomenal impact due to realization through digital implementation. Digital fractional order controllers have created wide scope as it possess the inherent advantages like robustness against the plant parameter variation. This paper provides brief design procedure of fractional order proportional-integral-derivative (FO-PID) controller through the indirect approach of approximation using constant phase technique. The new modified dynamic particle swarm optimization (IdPSO) technique is proposed to find controller parameters. The FO-PID controller is implemented using floating point digital signal processor. The building blocks are designed and assembled with all peripheral components for the 1.5kW industrial DC motor drive. The robust operation for parametric variation is ascertained by testing the controller with two separately excited DC motors with the same rating but different parameters. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved. 3. Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order International Nuclear Information System (INIS) He Qiu-Yan; Yuan Xiao; Yu Bo 2017-01-01 The performance analysis of the generalized Carlson iterating process, which can realize the rational approximation of fractional operator with arbitrary order, is presented in this paper. The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained. K-index, P-index, O-index, and complexity index are introduced to contribute to performance analysis. Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order, these rational approximation impedance functions calculated by the iterating function meet computational rationality, positive reality, and operational validity. Then they are capable of having the operational performance of fractional operators and being physical realization. The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited. (paper) 4. Chaos Suppression of an Electrically Actuated Microresonator Based on Fractional-Order Nonsingular Fast Terminal Sliding Mode Control Directory of Open Access Journals (Sweden) Jianxin Han 2017-01-01 Full Text Available This paper focuses on chaos suppression strategy of a microresonator actuated by two symmetrical electrodes. Dynamic behavior of this system under the case where the origin is the only stable equilibrium is investigated first. Numerical simulations reveal that system may exhibit chaotic motion under certain excitation conditions. Then, bifurcation diagrams versus amplitude or frequency of AC excitation are drawn to grasp system dynamics nearby its natural frequency. Results show that the vibration is complex and may exhibit period-doubling bifurcation, chaotic motion, or dynamic pull-in instability. For the suppression of chaos, a novel control algorithm, based on an integer-order nonsingular fast terminal sliding mode and a fractional-order switching law, is proposed. Fractional Lyapunov Stability Theorem is used to guarantee the asymptotic stability of the system. Finally, numerical results with both fractional-order and integer-order control laws show that our proposed control law is effective in controlling chaos with system uncertainties and external disturbances. 5. Dynamic stability analysis of fractional order leaky integrator echo state neural networks Science.gov (United States) Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A. 2017-06-01 The Leaky integrator echo state neural network (Leaky-ESN) is an improved model of the recurrent neural network (RNN) and adopts an interconnected recurrent grid of processing neurons. This paper presents a new proof for the convergence of a Lyapunov candidate function to zero when time tends to infinity by means of the Caputo fractional derivative with order lying in the range (0, 1). The stability of Fractional-Order Leaky-ESN (FO Leaky-ESN) is then analyzed, and the existence, uniqueness and stability of the equilibrium point are provided. A numerical example demonstrates the feasibility of the proposed method. 6. Fractional Order Modeling of Atmospheric Turbulence - A More Accurate Modeling Methodology for Aero Vehicles Science.gov (United States) Kopasakis, George 2014-01-01 The presentation covers a recently developed methodology to model atmospheric turbulence as disturbances for aero vehicle gust loads and for controls development like flutter and inlet shock position. The approach models atmospheric turbulence in their natural fractional order form, which provides for more accuracy compared to traditional methods like the Dryden model, especially for high speed vehicle. The presentation provides a historical background on atmospheric turbulence modeling and the approaches utilized for air vehicles. This is followed by the motivation and the methodology utilized to develop the atmospheric turbulence fractional order modeling approach. Some examples covering the application of this method are also provided, followed by concluding remarks. 7. Automated system for fractionation of blood samples Energy Technology Data Exchange (ETDEWEB) Lee, N. E.; Genung, R. K.; Johnson, W. F.; Mrochek, J. E.; Scott, C. D. 1978-01-01 A prototype system for preparing multiple fractions of blood components (plasma, washed red cells, and hemolysates) using automated techniques has been developed. The procedure is based on centrifugal separation and differential pressure-induced transfer in a rotor that has been designed to process numerous samples simultaneously. Red cells are sedimented against the outer walls of the sample chamber, and plasma is syphoned, by imposition of eithr a slight positive or negative pressure, into individual reservoirs in a collection ring. Washing of cells is performed in situ; samples of washed cells, either packed or in saline solution, can be recovered. Cellular hemolysates are prepared and automatically transferred to individual, commercially available collection vials ready for storage in liquid nitrogen or immediate analysis. The system has potential application in any biomedical area which requires high sample throughput and in which one or more of the blood fractions will be used. A separate unit has been designed and developed for the semiautomated cleaning of the blood processing vessel. 8. A uniform LMI formulation for tuning PID, multi-term fractional-order PID, and Tilt-Integral-Derivative (TID) for integer and fractional-order processes. Science.gov (United States) Merrikh-Bayat, Farshad 2017-05-01 In this paper first the Multi-term Fractional-Order PID (MFOPID) whose transfer function is equal to [Formula: see text] , where k j and α j are unknown and known real parameters respectively, is introduced. Without any loss of generality, a special form of MFOPID with transfer function k p +k i /s+k d1 s+k d2 s μ where k p , k i , k d1 , and k d2 are unknown real and μ is a known positive real parameter, is considered. Similar to PID and TID, MFOPID is also linear in its parameters which makes it possible to study all of them in a same framework. Tuning the parameters of PID, TID, and MFOPID based on loop shaping using Linear Matrix Inequalities (LMIs) is discussed. For this purpose separate LMIs for closed-loop stability (of sufficient type) and adjusting different aspects of the open-loop frequency response are developed. The proposed LMIs for stability are obtained based on the Nyquist stability theorem and can be applied to both integer and fractional-order (not necessarily commensurate) processes which are either stable or have one unstable pole. Numerical simulations show that the performance of the four-variable MFOPID can compete the trivial five-variable FOPID and often excels PID and TID. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved. 9. Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations. Science.gov (United States) Lorenzo, C F; Hartley, T T; Malti, R 2013-05-13 A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics. 10. Approximate solution of space and time fractional higher order phase field equation Science.gov (United States) Shamseldeen, S. 2018-03-01 This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated. 11. Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations Science.gov (United States) Gómez-Aguilar, J. F. 2018-03-01 In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking. 12. Boundary Value Problems for a Class of Sequential Integrodifferential Equations of Fractional Order Directory of Open Access Journals (Sweden) Bashir Ahmad 2013-01-01 Full Text Available We investigate the existence of solutions for a sequential integrodifferential equation of fractional order with some boundary conditions. The existence results are established by means of some standard tools of fixed point theory. An illustrative example is also presented. 13. Semilinear functional differential equations of fractional order with state-dependent delay OpenAIRE Mohamed Abdalla Darwish; Sotiris K. Ntouyas 2009-01-01 In this paper we study the existence of solutions for the initial value problem for semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Leray-Schauder type is the main tool in our analysis. 14. Semilinear functional differential equations of fractional order with state-dependent delay Directory of Open Access Journals (Sweden) Mohamed Abdalla Darwish 2009-03-01 Full Text Available In this paper we study the existence of solutions for the initial value problem for semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Leray-Schauder type is the main tool in our analysis. 15. A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations Directory of Open Access Journals (Sweden) Xiangbing Zhou 2012-01-01 Full Text Available We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010. We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives. 16. Dynamic behaviours and control of fractional-order memristor-based ... Indian Academy of Sciences (India) with cubic nonlinearities [11] by using discrete-component circuits mimicking ideal mem- ristor features. Circuital .... Consider a three-dimensional ordinary differential equations as. ˙x(t) = f (x, μ),. (5) where x .... Further, the bifurcation diagrams of state variable x vs. the fractional-order α is shown in figure 3. When α = 0.8,a ... 17. Integral equations of fractional order with multiple time delays in Banach spaces Directory of Open Access Journals (Sweden) Mouffak Benchohra 2012-04-01 Full Text Available In this article, we give sufficient conditions for the existence of solutions for an integral equation of fractional order with multiple time delays in Banach spaces. Our main tool is a fixed point theorem of Monch type associated with measures of noncompactness. Our results are illustrated by an example. 18. Higher Order Commutators of Fractional Integral Operator on the Homogeneous Herz Spaces with Variable Exponent Directory of Open Access Journals (Sweden) Liwei Wang 2013-01-01 Full Text Available By decomposing functions, we establish estimates for higher order commutators generated by fractional integral with BMO functions or the Lipschitz functions on the homogeneous Herz spaces with variable exponent. These estimates extend some known results in the literatures. 19. Multirate Fractional-Order Repetitive Control of Shunt Active Power Filter Suitable for Microgrid Applications DEFF Research Database (Denmark) Xie, Chuan; Zhao, Xin; Savaghebi, Mehdi 2017-01-01 This paper presents a multi-rate fractional-order repetitive control (MRFORC) scheme for three-phase shunt active power filter (APF). The proposed APF control scheme includes an inner proportional-integral (PI) control loop with a sampling rate identical to switching frequency and an external plug... 20. Enhanced fractional-order repetitive control for three-phase active power filter DEFF Research Database (Denmark) Xie, Chuan; Li, Kai; Zhao, Xin 2017-01-01 Fractional-order repetitive control (FORC) has been demonstrated to be able to offer high control accuracy for active power filters (APFs) to compensate the harmonics even in the presence of wide range grid frequency variations. However, the online coefficient update mechanism of the FORC, which... 1. Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate Directory of Open Access Journals (Sweden) Adnane Boukhouima 2017-01-01 Full Text Available We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results. 2. Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation International Nuclear Information System (INIS) Li, Gongsheng; Zhang, Dali; Jia, Xianzheng; Yamamoto, Masahiro 2013-01-01 This paper deals with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the fractional order in the 1D time-fractional diffusion equation with smooth initial functions by using boundary measurements. The uniqueness results for the inverse problem are proved on the basis of the inverse eigenvalue problem, and the Lipschitz continuity of the solution operator is established. A modified optimal perturbation algorithm with a regularization parameter chosen by a sigmoid-type function is put forward for the discretization of the minimization problem. Numerical inversions are performed for the diffusion coefficient taking on different functional forms and the additional data having random noise. Several factors which have important influences on the realization of the algorithm are discussed, including the approximate space of the diffusion coefficient, the regularization parameter and the initial iteration. The inversion solutions are good approximations to the exact solutions with stability and adaptivity demonstrating that the optimal perturbation algorithm with the sigmoid-type regularization parameter is efficient for the simultaneous inversion. (paper) 3. Robust fractional order sliding mode control of doubly-fed induction generator (DFIG)-based wind turbines. Science.gov (United States) Ebrahimkhani, Sadegh 2016-07-01 Wind power plants have nonlinear dynamics and contain many uncertainties such as unknown nonlinear disturbances and parameter uncertainties. Thus, it is a difficult task to design a robust reliable controller for this system. This paper proposes a novel robust fractional-order sliding mode (FOSM) controller for maximum power point tracking (MPPT) control of doubly fed induction generator (DFIG)-based wind energy conversion system. In order to enhance the robustness of the control system, uncertainties and disturbances are estimated using a fractional order uncertainty estimator. In the proposed method a continuous control strategy is developed to achieve the chattering free fractional order sliding-mode control, and also no knowledge of the uncertainties and disturbances or their bound is assumed. The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov׳s stability theory. Simulation results in the presence of various uncertainties were carried out to evaluate the effectiveness and robustness of the proposed control scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved. 4. Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay Directory of Open Access Journals (Sweden) S. J. Sadati 2010-01-01 Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems. 5. Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order Science.gov (United States) Sayevand, K.; Pichaghchi, K. 2018-04-01 In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer. 6. Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them Science.gov (United States) Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor) 2002-01-01 Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis. 7. Design Of Multivariable Fractional Order Pid Controller Using Covariance Matrix Adaptation Evolution Strategy Directory of Open Access Journals (Sweden) Sivananaithaperumal Sudalaiandi 2014-06-01 Full Text Available This paper presents an automatic tuning of multivariable Fractional-Order Proportional, Integral and Derivative controller (FO-PID parameters using Covariance Matrix Adaptation Evolution Strategy (CMAES algorithm. Decoupled multivariable FO-PI and FO-PID controller structures are considered. Oustaloup integer order approximation is used for the fractional integrals and derivatives. For validation, two Multi-Input Multi- Output (MIMO distillation columns described byWood and Berry and Ogunnaike and Ray are considered for the design of multivariable FO-PID controller. Optimal FO-PID controller is designed by minimizing Integral Absolute Error (IAE as objective function. The results of previously reported PI/PID controller are considered for comparison purposes. Simulation results reveal that the performance of FOPI and FO-PID controller is better than integer order PI/PID controller in terms of IAE. Also, CMAES algorithm is suitable for the design of FO-PI / FO-PID controller. 8. Maximum likelihood estimation of fractionally cointegrated systems DEFF Research Database (Denmark) Lasak, Katarzyna In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointe- gration relations, the degree of fractional cointegration, the matrix of the speed of adjustment to the equilib......In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointe- gration relations, the degree of fractional cointegration, the matrix of the speed of adjustment... 9. Experimental Characterization of Ionic Polymer Metal Composite as a Novel Fractional Order Element Directory of Open Access Journals (Sweden) Riccardo Caponetto 2013-01-01 Full Text Available Ionic polymer metal composites (IPMCs are electroactive materials made of ionic polymer thin membranes with platinum metallization on their surfaces. They are interesting materials due to not only their electromechanical applications as transducers but also to their electrochemical features and the relationship between the ionic/solvent current and the potential field. Their electrochemical properties thus suggest the possibility for exploiting them as compact fractional-order elements (FOEs with a view of defining fabrication processes and production strategies that assure the desired performances. In this paper, the experimental electrical characterization of a brand new IPMC setup in a fixed sandwich configuration is proposed. Two IPMC devices with different platinum absorption times (5 h and 20 h are characterized through experimental data: first, a preliminary linearity study is performed for a fixed input voltage amplitude in order to determine the frequency region where IPMC can be approximated as linear; then, a frequency analysis is carried out in order to identify a coherent fractional-order dynamics in the bode diagrams. Such analyses take the first steps towards a simplified model of IPMC as a compact electronic FOE for which the fractional exponent value depends on fabrication parameters as the absorption time. 10. The Immune System: the ultimate fractionated cyber-physical system Directory of Open Access Journals (Sweden) Carolyn Talcott 2013-09-01 Full Text Available In this little vision paper we analyze the human immune system from a computer science point of view with the aim of understanding the architecture and features that allow robust, effective behavior to emerge from local sensing and actions. We then recall the notion of fractionated cyber-physical systems, and compare and contrast this to the immune system. We conclude with some challenges. 11. Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations International Nuclear Information System (INIS) Chakraverty, S.; Tapaswini, Smita 2014-01-01 The fractional diffusion equation is one of the most important partial differential equations (PDEs) to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 < α ≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases. (general) 12. Closed-loop step response for tuning PID-fractional-order-filter controllers. Science.gov (United States) Amoura, Karima; Mansouri, Rachid; Bettayeb, Maâmar; Al-Saggaf, Ubaid M 2016-09-01 Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the fractional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved. 13. RDTM solution of Caputo time fractional-order hyperbolic telegraph equation Science.gov (United States) Srivastava, Vineet K.; Awasthi, Mukesh K.; Tamsir, Mohammad 2013-03-01 In this study, a mathematical model has been developed for the second order hyperbolic one-dimensional time fractional Telegraph equation (TFTE). The fractional derivative has been described in the Caputo sense. The governing equations have been solved by a recent reliable semi-analytic method known as the reduced differential transformation method (RDTM). The method is a powerful mathematical technique for solving wide range of problems. Using RDTM method, it is possible to find exact solution as well as closed approximate solution of any ordinary or partial differential equation. Three numerical examples of TFTE have been provided in order to check the effectiveness, accuracy and convergence of the method. The computed results are also depicted graphically. 14. Fractional order Darwinian particle swarm optimization applications and evaluation of an evolutionary algorithm CERN Document Server Couceiro, Micael 2015-01-01 This book examines the bottom-up applicability of swarm intelligence to solving multiple problems, such as curve fitting, image segmentation, and swarm robotics. It compares the capabilities of some of the better-known bio-inspired optimization approaches, especially Particle Swarm Optimization (PSO), Darwinian Particle Swarm Optimization (DPSO) and the recently proposed Fractional Order Darwinian Particle Swarm Optimization (FODPSO), and comprehensively discusses their advantages and disadvantages. Further, it demonstrates the superiority and key advantages of using the FODPSO algorithm, suc 15. Convergence analysis of homotopy perturbation method for Volterra integro-differential equations of fractional order Directory of Open Access Journals (Sweden) K. Sayevand 2013-12-01 Full Text Available Based on the homotopy perturbation method (HPM, a general analytical approach for obtaining approximate series solutions to Volterra integro-differential equations of fractional order is proposed. The approximate solutions are calculated in the form of a convergent series with easily computable components. In this paper, the uniqueness of the obtained solution and the convergence properties of the approach are studied. Some examples are presented, to verify convergence, and illustrating the efficiency and simplicity of the approach. 16. Global attractivity of solutions for a nonlinear functional integral equation of fractional order in Banach space Science.gov (United States) Karande, B. D. 2014-12-01 In this paper, we discuss the existence of solutions for a nonlinear functional integral equation of fractional order in R+ via a hybrid fixed point theorem due to B.C. Dhage. This equation will be carried out in the Banach space of real functions defined, continuous and bounded on an unbounded interval R+. Moreover, we show that solutions of this equation are uniformly globally attractive and uniformly globally asymptotically attractive on R+. 17. Monotonic solutions of functional integral and differential equations of fractional order Directory of Open Access Journals (Sweden) Ahmed El-Sayed 2009-02-01 Full Text Available The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equations have been studied by J. Banas. Here we are concerned with a singular quadratic functional integral equations. The existence of positive monotonic solutions$x \\in L_1[0,1]will be proved. The fractional order nonlinear functional differential equation will be given as a special case. 18. Lagrange α-exponential stability and α-exponential convergence for fractional-order complex-valued neural networks. Science.gov (United States) Jian, Jigui; Wan, Peng 2017-07-01 This paper deals with the problem on Lagrange α-exponential stability and α-exponential convergence for a class of fractional-order complex-valued neural networks. To this end, some new fractional-order differential inequalities are established, which improve and generalize previously known criteria. By using the new inequalities and coupling with the Lyapunov method, some effective criteria are derived to guarantee Lagrange α-exponential stability and α-exponential convergence of the addressed network. Moreover, the framework of the α-exponential convergence ball is also given, where the convergence rate is related to the parameters and the order of differential of the system. These results here, which the existence and uniqueness of the equilibrium points need not to be considered, generalize and improve the earlier publications and can be applied to monostable and multistable fractional-order complex-valued neural networks. Finally, one example with numerical simulations is given to show the effectiveness of the obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved. 19. Order Fulfillment and Accounting System Data.gov (United States) National Archives and Records Administration — OFAS is the financial management system that tracks and provides accounting of customer service requests for reproductions of National Archives and Records... 20. Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control Science.gov (United States) Ding, Da-Wei; Yan, Jie; Wang, Nian; Liang, Dong 2017-09-01 In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fractional order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more practical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective. Supported by National Natural Science Foundation of China under Grant No. 61201227, National Natural Science Foundation of China Guangdong Joint Fund under Grant No. U1201255, the Natural Science Foundation of Anhui Province under Grant No. 1208085MF93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B, and also supported by Chinese Scholarship Council 1. IPMSM velocity and current control using MTPA based adaptive fractional order sliding mode controller Directory of Open Access Journals (Sweden) Sayed Hamed Hosseini 2017-06-01 Full Text Available This paper presents a two-loop approach for velocity and stator currents control of an Interior-type Permanent Magnet Synchronous Motor (IPMSM. In the outer loop, the reference torque obtained from a conventional PI controller gives two-axis stator reference currents based on Maximum-Torque per Ampere (MTPA strategy. In the inner loop, an adaptive fractional order sliding mode controller is designed to reach the two-axis stator currents to their reference values obtained from the MTPA method. To achieve this idea, fractional order sliding surfaces and an adaptive controller with adjustable parameters are employed. The adaptive controller is designed to increase the robustness of the proposed method against the uncertainties in stator resistance and inductances. A Lyapunov based adaptation mechanism is proposed for adjustment of the controller parameters. The optimal value of the fractional orders are obtained by optimization of an integral time absolute error performance index. The simulation results show the robustness of the proposed method against the uncertainties in stator resistance and stator inductances. 2. Rayleigh–Lamb wave propagation on a fractional order viscoelastic plate Science.gov (United States) Meral, F. Can; Royston, Thomas J.; Magin, Richard L. 2011-01-01 A previous study of the authors published in this journal focused on mechanical wave motion in a viscoelastic material representative of biological tissue [Meral et al., J. Acoust. Soc. Am. 126, 3278–3285 (2009)]. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and sub-surface sources were considered. It was shown that a fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time, resulted in closer agreement with experiment as compared with conventional (integer order) models, such as those of Voigt and Zener. In the present study, this analysis is extended to another configuration and wave type: out-of-plane response of a viscoelastic plate to harmonic anti-symmetric Lamb wave excitation. Theoretical solutions are compared with experimental measurements for a polymeric tissue mimicking phantom material. As in the previous configurations the fractional order modeling assumption improves the match between theory and experiment over a wider frequency range. Experimental complexities in the present study and the reliability of the different approaches for quantifying the shear viscoelastic properties of the material are discussed. PMID:21361459 3. Symmetric, discrete fractional splines and Gabor systems DEFF Research Database (Denmark) Søndergaard, Peter Lempel 2006-01-01 In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continu......In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing...... the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases.... 4. Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions International Nuclear Information System (INIS) Jumarie, Guy 2009-01-01 A probability distribution of fractional (or fractal) order is defined by the measure μ{dx} = p(x)(dx) α , 0 α (D x α h α )f(x) provided by the modified Riemann Liouville definition, one can expand a probability calculus parallel to the standard one. A Fourier's transform of fractional order using the Mittag-Leffler function is introduced, together with its inversion formula; and it provides a suitable generalization of the characteristic function of fractal random variables. It appears that the state moments of fractional order are more especially relevant. The main properties of this fractional probability calculus are outlined, it is shown that it provides a sound approach to Fokker-Planck equation which are fractional in both space and time, and it provides new results in the information theory of non-random functions. 5. Experimental verification of on-chip CMOS fractional-order capacitor emulators KAUST Repository Tsirimokou, G. 2016-06-13 The experimental results from a fabricated integrated circuit of fractional-order capacitor emulators are reported. The chip contains emulators of capacitors of orders 0.3, 0.4, 0.5, 0.6 and 0.7 with nano-Farad pseudo-capacitances that can be adjusted through a bias current. Two off-chip capacitors are used to set the bandwidth of each emulator independently. The chip was designed in Austria microsystems (AMS) 0.35μ CMOS. © 2016 The Institution of Engineering and Technology. 6. Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model. Directory of Open Access Journals (Sweden) Seth H Weinberg Full Text Available Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity. 7. Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model. Science.gov (United States) Weinberg, Seth H 2015-01-01 Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity. 8. Existence of a coupled system of fractional differential equations Energy Technology Data Exchange (ETDEWEB) Ibrahim, Rabha W. [Multimedia unit, Department of Computer System and Technology Faculty of Computer Science & IT, University of Malaya, 50603 Kuala Lumpur (Malaysia); Siri, Zailan [Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia) 2015-10-22 We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator. 9. Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law Science.gov (United States) Želi, Velibor; Zorica, Dušan 2018-02-01 Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws. 10. Comparisons of Modeling and State of Charge Estimation for Lithium-Ion Battery Based on Fractional Order and Integral Order Methods Directory of Open Access Journals (Sweden) Renxin Xiao 2016-03-01 Full Text Available In order to properly manage lithium-ion batteries of electric vehicles (EVs, it is essential to build the battery model and estimate the state of charge (SOC. In this paper, the fractional order forms of Thevenin and partnership for a new generation of vehicles (PNGV models are built, of which the model parameters including the fractional orders and the corresponding resistance and capacitance values are simultaneously identified based on genetic algorithm (GA. The relationships between different model parameters and SOC are established and analyzed. The calculation precisions of the fractional order model (FOM and integral order model (IOM are validated and compared under hybrid test cycles. Finally, extended Kalman filter (EKF is employed to estimate the SOC based on different models. The results prove that the FOMs can simulate the output voltage more accurately and the fractional order EKF (FOEKF can estimate the SOC more precisely under dynamic conditions. 11. Laser systems for ablative fractional resurfacing DEFF Research Database (Denmark) Paasch, Uwe; Haedersdal, Merete 2011-01-01 Ablative fractional resurfacing (AFR) creates microscopic vertical ablated channels that are surrounded by a thin layer of coagulated tissue, constituting the microscopic treatment zones (MTZs). AFR induces epidermal and dermal remodeling, which raises new possibilities for the treatment...... of a variety of skin conditions, primarily chronically photodamaged skin, but also acne and burn scars. In addition, it is anticipated that AFR can be utilized in the laser-assisted delivery of topical drugs. Clinical efficacy coupled with minimal downtime has driven the development of various fractional... 12. Research and Application on Fractional-Order Darwinian PSO Based Adaptive Extended Kalman Filtering Algorithm Directory of Open Access Journals (Sweden) Qiguang Zhu 2014-05-01 Full Text Available To resolve the difficulty in establishing accurate priori noise model for the extended Kalman filtering algorithm, propose the fractional-order Darwinian particle swarm optimization (PSO algorithm has been proposed and introduced into the fuzzy adaptive extended Kalman filtering algorithm. The natural selection method has been adopted to improve the standard particle swarm optimization algorithm, which enhanced the diversity of particles and avoided the premature. In addition, the fractional calculus has been used to improve the evolution speed of particles. The PSO algorithm after improved has been applied to train fuzzy adaptive extended Kalman filter and achieve the simultaneous localization and mapping. The simulation results have shown that compared with the geese particle swarm optimization training of fuzzy adaptive extended Kalman filter localization and mapping algorithm, has been greatly improved in terms of localization and mapping. 13. Intelligent fractions learning system: conceptual design CSIR Research Space (South Africa) Laine, TH 2010-01-01 Full Text Available UFractions is a ubiquitous learning environment which combines mobile technology, tangible fraction blocks and a story-based game into a mathematical learning experience. In this paper the authors present a novel concept for monitoring a user’s... 14. Two efficient reliable methods for solving fractional fifth order modified Sawada–Kotera equation appearing in mathematical physics OpenAIRE S. Saha Ray; S. Sahoo 2016-01-01 The present paper deals with two reliable efficient methods viz. tanh-sech method and modified Kudryashov method, which are used to solve time-fractional nonlinear evolution equation. For delineating the legitimacy of proposed methods, we employ it to the time-fractional fifth-order modified Sawada–Kotera equations. As a consequence, we effectively obtained more new exact solutions for time-fractional fifth-order modified Sawada–Kotera equation. We have also presented the numerical simulation... 15. Synchronous Generator Model with Fractional Order Voltage Regulator PIbDa Directory of Open Access Journals (Sweden) Dariusz Spałek 2015-06-01 Full Text Available Synchronous generator together with excitation circuit, voltage controller and system stabilizer constitute nonlinear ordinary differential equations set. The nonlinearity of differential equations set results from magnetic circuits saturation. One of the most important, from the electric energy distribution point of view, is the influence of voltage control applied on the generator voltage. There could be applied regulator either classical PID or fractional of type PIbDa which bases on the so-called fractional derivative idea. Numerical solutions of nonlinear differential equations set, that takes into account both magnetic circuits saturation and fractional regulator PIbDa, lead to decisions either to accept or to reject the chosen parameters. The sensibility of generator work on chosen fractional regulator parameters is the main aim of this paper. With the help of C++ program provided the most important states of work (short–circuit, setting voltage change, reactive power rejection can be analyzed basing on the accepted model of synchronous generator such as (1,1, (2,2 or (3,3. 16. The generalization of Plackett-Burman design based on fractional calculus of complex order Science.gov (United States) Ibrahim, Rabha W.; Jalab, Hamid A. 2014-12-01 Response surface attitude was working to optimize the degradation situations of Aflatoxin B1(AFB1) by Rhodococcus erythropolis in liquid culture. The interesting factors that influence the degradation, as identified by a Plackett-Burman design with six variables, were temperature, liquid volume, pH, inoculums size, agitation speed and incubation time. In this work, we generalize the Plackett-Burman design, based on fractional calculus of complex order, to describe correlation between the six variables and the degradation rate of AFB1. The experimental results show the influence of the proposed method. The results demonstrated that the degradation efficiency of R. erythropolis could extent 99% in liquid culture. 17. Classification of fractional order biomarkers for anomalous diffusion using q-space entropy. Science.gov (United States) Magin, Richard L; Ingo, Carson; Triplett, William; Colon-Perez, Louis; Mareci, Tom H 2014-01-01 In this study, we applied continuous random walk theory (CTRW) to develop a new model that characterizes anomalous diffusion in magnetic resonance imaging experiments. Furthermore, we applied a classification scheme based on information theoretic a techniques to characterize the degree of heterogeneity and complexity in biological tissues. From a CTRW approach, the Fourier transform of the generalized solution to the diffusion equation comes in the form of the Mittag-Leffler function. In this solution form, the relative stochastic uncertainty in the diffusion process can be computed with spectral entropy. We interrogated both white and gray matter regions of a fixed rat brain with diffusion - weighted magnetic resonance imaging experiments up to 26,000 s/mm² by independently weighting q and Δ. to investigate the effects on the diffusion phenomena. Our model fractional order parameters, α and β, and entropy measure, H(q, Δ), differentiated between tissue types and extracted differing information within a region of interest based on the type of diffusion experiment performed. By combining fractional order modeling and information theory, new and powerful biomarkers are available to characterize tissue microstructure and provide contextual information about the anatomical complexity. 18. Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization Science.gov (United States) Pang, Guofei; Perdikaris, Paris; Cai, Wei; Karniadakis, George Em 2017-11-01 The fractional advection-dispersion equation (FADE) can describe accurately the solute transport in groundwater but its fractional order has to be determined a priori. Here, we employ multi-fidelity Bayesian optimization to obtain the fractional order under various conditions, and we obtain more accurate results compared to previously published data. Moreover, the present method is very efficient as we use different levels of resolution to construct a stochastic surrogate model and quantify its uncertainty. We consider two different problem set ups. In the first set up, we obtain variable fractional orders of one-dimensional FADE, considering both synthetic and field data. In the second set up, we identify constant fractional orders of two-dimensional FADE using synthetic data. We employ multi-resolution simulations using two-level and three-level Gaussian process regression models to construct the surrogates. 19. Stochastic resonance in overdamped systems with fractional power nonlinearity Science.gov (United States) Yang, Jianhua; Sanjuán, Miguel A. F.; Chen, Pengpeng; Liu, Houguang 2017-10-01 The stochastic resonance phenomenon in overdamped systems with fractional power nonlinearity is thoroughly investigated. The first kind of nonlinearity is a general fractional power function. The second kind of nonlinearity is a fractional power function with deflection. For the first case, the response is clearly divergent for some fractional exponent values. The curve of the spectral amplification factor versus the fractional exponent presents some discrete regions. For the second case, the response will not be divergent for any fractional exponent value. The spectral amplification factor decreases with the increase in the fractional exponent. For both cases, the nonlinearity is the necessary ingredient to induce stochastic resonance. However, it is not the sufficient cause to amplify the weak signal. On the one hand, the noise cannot induce stochastic resonance in the corresponding linear system. On the other hand, the spectral amplification factor of the nonlinear system is lower than that of the corresponding linear system. Through the analysis carried out in this paper, we are able to find that the system with fractional deflection nonlinearity is a better stochastic resonance system, especially when an appropriate exponent value is chosen. The results in this paper might have a certain reference value for signal processing problems in relation with the stochastic resonance method. 20. Synchronisation, electronic circuit implementation, and fractional-order analysis of 5D ordinary differential equations with hidden hyperchaotic attractors Science.gov (United States) Wei, Zhouchao; Rajagopal, Karthikeyan; Zhang, Wei; Kingni, Sifeu Takougang; Akgül, Akif 2018-04-01 Hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed 5D hyperchaotic Burke-Shaw system with only one stable equilibrium. To the best of our knowledge, this feature has rarely been previously reported in any other higher-dimensional systems. Unidirectional linear error feedback coupling scheme is used to achieve hyperchaos synchronisation, which will be estimated by using two indicators: the normalised average root-mean squared synchronisation error and the maximum cross-correlation coefficient. The 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integration. In addition, fractional-order hidden hyperchaotic system will be considered from the following three aspects: stability, bifurcation analysis and FPGA implementation. Such implementations in real time represent hidden hyperchaotic attractors with important consequences for engineering applications. 1. Fractional order integration and fuzzy logic based filter for denoising of echocardiographic image. Science.gov (United States) Saadia, Ayesha; Rashdi, Adnan 2016-12-01 Ultrasound is widely used for imaging due to its cost effectiveness and safety feature. However, ultrasound images are inherently corrupted with speckle noise which severely affects the quality of these images and create difficulty for physicians in diagnosis. To get maximum benefit from ultrasound imaging, image denoising is an essential requirement. To perform image denoising, a two stage methodology using fuzzy weighted mean and fractional integration filter has been proposed in this research work. In stage-1, image pixels are processed by applying a 3 × 3 window around each pixel and fuzzy logic is used to assign weights to the pixels in each window, replacing central pixel of the window with weighted mean of all neighboring pixels present in the same window. Noise suppression is achieved by assigning weights to the pixels while preserving edges and other important features of an image. In stage-2, the resultant image is further improved by fractional order integration filter. Effectiveness of the proposed methodology has been analyzed for standard test images artificially corrupted with speckle noise and real ultrasound B-mode images. Results of the proposed technique have been compared with different state-of-the-art techniques including Lsmv, Wiener, Geometric filter, Bilateral, Non-local means, Wavelet, Perona et al., Total variation (TV), Global Adaptive Fractional Integral Algorithm (GAFIA) and Improved Fractional Order Differential (IFD) model. Comparison has been done on quantitative and qualitative basis. For quantitative analysis different metrics like Peak Signal to Noise Ratio (PSNR), Speckle Suppression Index (SSI), Structural Similarity (SSIM), Edge Preservation Index (β) and Correlation Coefficient (ρ) have been used. Simulations have been done using Matlab. Simulation results of artificially corrupted standard test images and two real Echocardiographic images reveal that the proposed method outperforms existing image denoising techniques 2. Boundedness, Mittag-Leffler stability and asymptotical ω-periodicity of fractional-order fuzzy neural networks. Science.gov (United States) Wu, Ailong; Zeng, Zhigang 2016-02-01 We show that the ω-periodic fractional-order fuzzy neural networks cannot generate non-constant ω-periodic signals. In addition, several sufficient conditions are obtained to ascertain the boundedness and global Mittag-Leffler stability of fractional-order fuzzy neural networks. Furthermore, S-asymptotical ω-periodicity and global asymptotical ω-periodicity of fractional-order fuzzy neural networks is also characterized. The obtained criteria improve and extend the existing related results. To illustrate and compare the theoretical criteria, some numerical examples with simulation results are discussed in detail. Crown Copyright © 2015. Published by Elsevier Ltd. All rights reserved. 3. Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation Science.gov (United States) Mohebbi, Akbar 2018-02-01 In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones. 4. Fractional monodromy in systems with coupled angular momenta DEFF Research Database (Denmark) Hansen, Mikael Sonne; Faure, F.; Zhilinskii, B.I. 2007-01-01 We present a one-parameter family of systems with fractional monodromy, which arises from a 1:2 diagonal action of a dynamical symmetry SO(2). In a regime of adiabatic separation of slow and fast motions, we relate the presence of fractional monodromy to a redistribution of states both... 5. Global Regularity for the Fractional Euler Alignment System Science.gov (United States) Do, Tam; Kiselev, Alexander; Ryzhik, Lenya; Tan, Changhui 2018-04-01 We study a pressureless Euler system with a non-linear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density dependence is natural: the alignment rate increases in the areas of high density due to species discomfort. The diffusive term has the order of a fractional Laplacian {(-partial _{xx})^{α/2}, α \\in (0, 1)}. The corresponding Burgers equation with a linear dissipation of this type develops shocks in a finite time. We show that the alignment nonlinearity enhances the dissipation, and the solutions are globally regular for all {α \\in (0, 1)}. To the best of our knowledge, this is the first example of such regularization due to the non-local nonlinear modulation of dissipation. 6. Repetitive transient extraction for machinery fault diagnosis using multiscale fractional order entropy infogram Science.gov (United States) Xu, Xuefang; Qiao, Zijian; Lei, Yaguo 2018-03-01 The presence of repetitive transients in vibration signals is a typical symptom of local faults of rotating machinery. Infogram was developed to extract the repetitive transients from vibration signals based on Shannon entropy. Unfortunately, the Shannon entropy is maximized for random processes and unable to quantify the repetitive transients buried in heavy random noise. In addition, the vibration signals always contain multiple intrinsic oscillatory modes due to interaction and coupling effects between machine components. Under this circumstance, high values of Shannon entropy appear in several frequency bands or high value of Shannon entropy doesn't appear in the optimal frequency band, and the infogram becomes difficult to interpret. Thus, it also becomes difficult to select the optimal frequency band for extracting the repetitive transients from the whole frequency bands. To solve these problems, multiscale fractional order entropy (MSFE) infogram is proposed in this paper. With the help of MSFE infogram, the complexity and nonlinear signatures of the vibration signals can be evaluated by quantifying spectral entropy over a range of scales in fractional domain. Moreover, the similarity tolerance of MSFE infogram is helpful for assessing the regularity of signals. A simulation and two experiments concerning a locomotive bearing and a wind turbine gear are used to validate the MSFE infogram. The results demonstrate that the MSFE infogram is more robust to the heavy noise than infogram and the high value is able to only appear in the optimal frequency band for the repetitive transient extraction. 7. The Effect of Magnetic Field and Initial Stress on Fractional Order Generalized Thermoelastic Half-Space Directory of Open Access Journals (Sweden) Sunita Deswal 2013-01-01 Full Text Available The aim of this paper is to study magneto-thermoelastic interactions in an initially stressed isotropic homogeneous half-space in the context of fractional order theory of generalized thermoelasticity. State space formulation with the Laplace transform technique is used to obtain the general solution, and the resulting formulation is applied to the ramp type increase in thermal load and zero stress. Solutions of the problem in the physical domain are obtained by using a numerical method of the Laplace inverse transform based on the Fourier expansion technique, and the expressions for the displacement, temperature, and stress inside the half-space are obtained. Numerical computations are carried out for a particular material for illustrating the results. Results obtained for the field variables are displayed graphically. Some comparisons have been shown in figures to present the effect of fractional parameter, ramp parameter, magnetic field, and initial stress on the field variables. Some particular cases of special interest have been deduced from the present investigation. 8. Robust Finite-Time Stabilization of Fractional-Order Neural Networks With Discontinuous and Continuous Activation Functions Under Uncertainty. Science.gov (United States) Ding, Zhixia; Zeng, Zhigang; Wang, Leimin 2017-03-10 This paper is concerned with robust finite-time stabilization for a class of fractional-order neural networks (FNNs) with two types of activation functions (i.e., discontinuous and continuous activation function) under uncertainty. It is worth noting that there exist few results about FNNs with discontinuous activation functions, which is mainly because classical solutions and theories of differential equations cannot be applied in this case. Especially, there is no relevant finite-time stabilization research for such system, and this paper makes up for the gap. The existence of global solution under the framework of Filippov for such system is guaranteed by limiting discontinuous activation functions. According to set-valued analysis and Kakutani's fixed point theorem, we obtain the existence of equilibrium point. In particular, based on differential inclusion theory and fractional Lyapunov stability theory, several new sufficient conditions are given to ensure finite-time stabilization via a novel discontinuous controller, and the upper bound of the settling time for stabilization is estimated. In addition, we analyze the finite-time stabilization of FNNs with Lipschitz-continuous activation functions under uncertainty. The results of this paper improve corresponding ones of integer-order neural networks with discontinuous and continuous activation functions. Finally, three numerical examples are given to show the effectiveness of the theoretical results. 9. Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload. Science.gov (United States) Sharma, Richa; Gaur, Prerna; Mittal, A P 2015-09-01 The robotic manipulators are multi-input multi-output (MIMO), coupled and highly nonlinear systems. The presence of external disturbances and time-varying parameters adversely affects the performance of these systems. Therefore, the controller designed for these systems should effectively deal with such complexities, and it is an intriguing task for control engineers. This paper presents two-degree of freedom fractional order proportional-integral-derivative (2-DOF FOPID) controller scheme for a two-link planar rigid robotic manipulator with payload for trajectory tracking task. The tuning of all controller parameters is done using cuckoo search algorithm (CSA). The performance of proposed 2-DOF FOPID controllers is compared with those of their integer order designs, i.e., 2-DOF PID controllers, and with the traditional PID controllers. In order to show effectiveness of proposed scheme, the robustness testing is carried out for model uncertainties, payload variations with time, external disturbance and random noise. Numerical simulation results indicate that the 2-DOF FOPID controllers are superior to their integer order counterparts and the traditional PID controllers. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved. 10. Laser beam pointing and stabilization by fractional-order PID control: Tuning rule and experiments KAUST Repository Al-Alwan, Asem Ibrahim Alwan 2017-10-24 This paper studies the problem of high-precision positioning of laser beams by using a robust Fractional-Order Proportional-Integral-Derivative (FOPID) controller. The control problem addressed in laser beams aims to maintain the position of the laser beam on a Position Sensing Device (PSD) despite the effects of noise and active disturbances. The FOPID controller is well known for its simplicity with better tuning flexibility along with robustness to noise and output disturbance rejections. Thus, a control strategy based on FOPID to achieve the control objectives has been proposed. The FOPID gains and differentiation orders are optimally tuned in order to fulfill the robustness design specifications by solving a nonlinear optimization problem. A comparison to the conventional Proportional-Integral-Derivative (PID) and robust PID is also provided from simulation and experiment set-up. Due to sensor noise, practical PID controllers that filter the position signal before taking the derivative have been also proposed. Experimental results show that the requirements are totally met for the laser beam platform to be stabilized. 11. The Study of Fractional Order Controller with SLAM in the Humanoid Robot Directory of Open Access Journals (Sweden) Shuhuan Wen 2014-01-01 Full Text Available We present a fractional order PI controller (FOPI with SLAM method, and the proposed method is used in the simulation of navigation of NAO humanoid robot from Aldebaran. We can discretize the transfer function by the Al-Alaoui generating function and then get the FOPI controller by Power Series Expansion (PSE. FOPI can be used as a correction part to reduce the accumulated error of SLAM. In the FOPI controller, the parameters (Kp,Ki, and α need to be tuned to obtain the best performance. Finally, we compare the results of position without controller and with PI controller, FOPI controller. The simulations show that the FOPI controller can reduce the error between the real position and estimated position. The proposed method is efficient and reliable for NAO navigation. 12. Optimal Trajectory Tracking Control for a Wheeled Mobile Robot Using Fractional Order PID Controller Directory of Open Access Journals (Sweden) Ameer L. Saleh 2018-02-01 Full Text Available This paper present an optimal Fractional Order PID (FOPID controller based on Particle Swarm Optimization (PSO for controlling the trajectory tracking of Wheeled Mobile Robot(WMR.The issue of trajectory tracking with given a desired reference velocity is minimized to get the distance and deviation angle equal to zero, to realize the objective of trajectory tracking a two FOPID controllers are used for velocity control and azimuth control to implement the trajectory tracking control. A path planning and path tracking methodologies are used to give different desired tracking trajectories. PSO algorithm is using to find the optimal parameters of FOPID controllers. The kinematic and dynamic models of wheeled mobile robot for desired trajectory tracking with PSO algorithm are simulated in Simulink-Matlab. Simulation results show that the optimal FOPID controllers are more effective and has better dynamic performance than the conventional methods. 13. A Novel Fractional-Order PID Controller for Integrated Pressurized Water Reactor Based on Wavelet Kernel Neural Network Algorithm Directory of Open Access Journals (Sweden) Yu-xin Zhao 2014-01-01 Full Text Available This paper presents a novel wavelet kernel neural network (WKNN with wavelet kernel function. It is applicable in online learning with adaptive parameters and is applied on parameters tuning of fractional-order PID (FOPID controller, which could handle time delay problem of the complex control system. Combining the wavelet function and the kernel function, the wavelet kernel function is adopted and validated the availability for neural network. Compared to the conservative wavelet neural network, the most innovative character of the WKNN is its rapid convergence and high precision in parameters updating process. Furthermore, the integrated pressurized water reactor (IPWR system is established by RELAP5, and a novel control strategy combining WKNN and fuzzy logic rule is proposed for shortening controlling time and utilizing the experiential knowledge sufficiently. Finally, experiment results verify that the control strategy and controller proposed have the practicability and reliability in actual complicated system. 14. Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation OpenAIRE Li, Zhiyuan; Yamamoto, Masahiro 2014-01-01 This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof. 15. Default settings of computerized physician order entry system order sets drive ordering habits. Science.gov (United States) Olson, Jordan; Hollenbeak, Christopher; Donaldson, Keri; Abendroth, Thomas; Castellani, William 2015-01-01 Computerized physician order entry (CPOE) systems are quickly becoming ubiquitous, and groups of orders ("order sets") to allow for easy order input are a common feature. This provides a streamlined mechanism to view, modify, and place groups of related orders. This often serves as an electronic equivalent of a specialty requisition. A characteristic, of these order sets is that specific orders can be predetermined to be "preselected" or "defaulted-on" whenever the order set is used while others are "optional" or "defaulted-off" (though there is typically the option is to "deselect" defaulted-on tests in a given situation). While it seems intuitive that the defaults in an order set are often accepted, additional study is required to understand the impact of these "default" settings in an order set on ordering habits. This study set out to quantify the effect of changing the default settings of an order set. For quality improvement purposes, order sets dealing with transfusions were recently reviewed and modified to improve monitoring of outcome. Initially, the order for posttransfusion hematocrits and platelet count had the default setting changed from "optional" to "preselected." The default settings for platelet count was later changed back to "optional," allowing for a natural experiment to study the effect of the default selections of an order set on clinician ordering habits. Posttransfusion hematocrit values were ordered for 8.3% of red cell transfusions when the default order set selection was "off" and for 57.4% of transfusions when the default selection was "preselected" (P default order set selection was "optional," increased to 59.4% when the default was changed to "preselected" (P default selection was returned to "optional." The posttransfusion platelet count rates during the two "optional" periods: 7.0% versus 7.5% - were not statistically different (P = 0.620). Default settings in CPOE order sets can significantly influence physician selection of 16. Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation Science.gov (United States) Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad 2017-07-01 This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme. 17. Fractionated spacecraft : The new sprout in distributed space systems NARCIS (Netherlands) Guo, J.; Maessen, D.C.; Gill, E.K.A. 2009-01-01 This paper provides a survey of current state-of-the-art technologies of fractionated spacecraft, a new architecture for distributed space systems. The survey covers six aspects: architecture, networking, wireless communication, wireless power transfer, distributed computing, and planned missions 18. Fractionation of Boron Isotopes in Icelandic Hydrothermal Systems Energy Technology Data Exchange (ETDEWEB) Aggarwal, J.K.; Palmer, M.R. 1995-01-01 Boron isotope ratios have been determined in a variety of different geothermal waters from hydrothermal systems across Iceland. Isotope ratios from the high temperature meteoric water recharged systems reflect the isotope ratio of the host rocks without any apparent fractionation. Seawater recharged geothermal systems exhibit more positive {delta}{sup 11}B values than the meteoric water recharged geothermal systems. Water/rock ratios can be assessed from boron isotope ratios in the saline hydrothermal systems. Low temperature hydrothermal systems also exhibit more positive {delta}{sup 11}B than the high temperature systems, indicating fractionation of boron due to adsorption of the lighter isotope onto secondary minerals. Fractionation of boron in carbonate deposits may indicate the level of equilibrium attained within the systems. 19. Response of MDOF strongly nonlinear systems to fractional Gaussian noises Energy Technology Data Exchange (ETDEWEB) Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn [Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China) 2016-08-15 In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems. 20. Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada-Kotera-Ito equation Science.gov (United States) Yaşar, Emrullah; Yıldırım, Yakup; Khalique, Chaudry Masood In this paper Lie symmetry analysis of the seventh-order time fractional Sawada-Kotera-Ito (FSKI) equation with Riemann-Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi-Kober sense. Furthermore, adapting the Ibragimov's nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method. 1. Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM. Science.gov (United States) Singh, Brajesh K; Srivastava, Vineet K 2015-04-01 The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. 2. Design of a fractional order PID controller using GBMO algorithm for load-frequency control with governor saturation consideration. Science.gov (United States) Zamani, Abbasali; Barakati, S Masoud; Yousofi-Darmian, Saeed 2016-09-01 Load-frequency control is one of the most important issues in power system operation. In this paper, a Fractional Order PID (FOPID) controller based on Gases Brownian Motion Optimization (GBMO) is used in order to mitigate frequency and exchanged power deviation in two-area power system with considering governor saturation limit. In a FOPID controller derivative and integrator parts have non-integer orders which should be determined by designer. FOPID controller has more flexibility than PID controller. The GBMO algorithm is a recently introduced search method that has suitable accuracy and convergence rate. Thus, this paper uses the advantages of FOPID controller as well as GBMO algorithm to solve load-frequency control. However, computational load will higher than conventional controllers due to more complexity of design procedure. Also, a GBMO based fuzzy controller is designed and analyzed in detail. The performance of the proposed controller in time domain and its robustness are verified according to comparison with other controllers like GBMO based fuzzy controller and PI controller that used for load-frequency control system in confronting with model parameters variations. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved. 3. Diffusion in ordered binary solid systems International Nuclear Information System (INIS) Stolwijk, N.A. 1980-01-01 This thesis contains contributions to the field of diffusion in ordered binary solid systems. An extensive experimental investigation of the self diffusion in CoGa is presented. The results of these diffusion measurements strongly suggest that a substantial part of the atomic migration is caused by a new type of defect. A quantitative description of the atomic displacements via this defect is given. Finally computer simulations are presented of diffusion and ordering in binary solid systems. (Auth.) 4. Systemic Design for Second-Order Effects Directory of Open Access Journals (Sweden) Evan Barba 2017-04-01 Full Text Available Second-order effects refer to changes within a system that are the result of changes made somewhere else in the system (the first-order effects. Second-order effects can occur at different spatial, temporal, or organizational scales from the original interventions, and are difficult to control. Some organizational theorists suggest that careful management of feedback processes can facilitate controlled change from one organizational configuration to another. Recognizing that skill in managing feedback processes is a core competency of design suggests that design skills are potentially useful tools in achieving organizational change. This paper describes a case study in which a co-design methodology was used to control the second-order effects resulting from a classroom intervention to create organizational change. This approach is then theorized as the Instigator Systems approach. 5. Functional fractional calculus for system identification and controls CERN Document Server Das, Shantanu 2008-01-01 This work is inspired by thought to have an overall fuel-ef?cient nuclear plant control system. I picked up the topic in 2002 while deriving the reactor control laws, which aimed at fuel ef?ciency. Controlling the nuclear reactor close to its natural behavior by concept of exponent shape governor, ratio control and use of logarithmic logic, aims at the fuel ef?ciency. The power-maneuvering trajectory is obtained by shaped-normalized-period function, and this de?nes the road map on which the reactor should be governed. The experience of this concept governing the Atomic Power Plant of Tarapur Atomic Power Station gives lesser overall gains compared to the older plants, where conventional proportional integral and deri- tive type (PID) scheme is employed. Therefore, this motivation led to design the scheme for control system than the conventional schemes to aim at overall plant ef?ciency. Thus, I felt the need to look beyondPID and obtained the answer in fr- tional order control system, requiring fractional cal... 6. Characterization of Anomalous Diffusion in Porous Biological Tissues Using Fractional Order Derivatives and Entropy. Science.gov (United States) Magin, Richard L; Ingo, Carson; Colon-Perez, Luis; Triplett, William; Mareci, Thomas H 2013-09-15 In this high-resolution magnetic resonance imaging (MRI) study at 17.6 Tesla of a fixed rat brain, we used the continuous time random walk theory (CTRW) for Brownian motion to characterize anomalous diffusion. The complex mesoporus structure of biological tissues (membranes, organelles, and cells) perturbs the motion of the random walker (water molecules in proton MRI) introducing halts between steps (waiting times) and restrictions on step sizes (jump lengths). When such waiting times and jump lengths are scaled with probability distributions that follow simple inverse power laws ( t -(1+α) , | x | -(1+β) ) non-Gaussian motion gives rise to sub- and super- diffusion. In the CTRW approach, the Fourier transform yields a solution to the generalized diffusion equation that can be expressed by the Mittag-Leffler function (MLF), E α (- D α, β | q | β Δ α ). We interrogated both white and gray matter regions in a 1 mm slice of a fixed rat brain (190 μ m in plane resolution) with diffusion weighted MRI experiments using b -values up to 25,000 s / mm 2 , by independently varying q and Δ. When fitting these data to our model, the fractional order parameters, α and β, and the entropy measure, [Formula: see text], were found to provide excellent contrast between white and gray matter and to give results that were sensitive to the type of diffusion experiment performed. 7. Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system Science.gov (United States) Huang, Chengdai; Cao, Jinde 2017-05-01 This paper is concerned with the issues of synchronization and anti-synchronization for fractional chaotic financial system with market confidence by taking advantage of active control approach. Some sufficient conditions are derived to guarantee the synchronization and anti-synchronization for the proposed fractional system. Moreover, the relationship between the order and synchronization(anti-synchronization) is demonstrated numerically. It reveals that synchronization(anti-synchronization) is faster as the order increases. Finally, two illustrative examples are exploited to verify the efficiency of the obtained theoretical results. 8. Existence of solutions to differential inclusions with fractional order and impulses Directory of Open Access Journals (Sweden) Mouffak Benchohra 2010-06-01 Full Text Available We establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values. The topological structure of the set of solutions is also considered. 9. Rapid Estimation Method for State of Charge of Lithium-Ion Battery Based on Fractional Continual Variable Order Model Directory of Open Access Journals (Sweden) Xin Lu 2018-03-01 Full Text Available In recent years, the fractional order model has been employed to state of charge (SOC estimation. The non integer differentiation order being expressed as a function of recursive factors defining the fractality of charge distribution on porous electrodes. The battery SOC affects the fractal dimension of charge distribution, therefore the order of the fractional order model varies with the SOC at the same condition. This paper proposes a new method to estimate the SOC. A fractional continuous variable order model is used to characterize the fractal morphology of charge distribution. The order identification results showed that there is a stable monotonic relationship between the fractional order and the SOC after the battery inner electrochemical reaction reaches balanced. This feature makes the proposed model particularly suitable for SOC estimation when the battery is in the resting state. Moreover, a fast iterative method based on the proposed model is introduced for SOC estimation. The experimental results showed that the proposed iterative method can quickly estimate the SOC by several iterations while maintaining high estimation accuracy. 10. Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems. Science.gov (United States) Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A 2016-01-01 This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval α ∈(0,1] and the Caputo definition for fractional derivatives is used. The boundedness of the solutions is proved for all three cases, and the convergence to zero of the mean value of one of the variables is also proved. Applications of the obtained results to fractional adaptive schemes in the context of identification and control problems are presented at the end of the paper, including numerical simulations which support the analytical results. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved. 11. Multiscale KF Algorithm for Strong Fractional Noise Interference Suppression in Discrete-Time UWB Systems Directory of Open Access Journals (Sweden) Liyun Su 2011-01-01 Full Text Available In order to suppress the interference of the strong fractional noise signal in discrete-time ultrawideband (UWB systems, this paper presents a new UWB multi-scale Kalman filter (KF algorithm for the interference suppression. This approach solves the problem of the narrowband interference (NBI as nonstationary fractional signal in UWB communication, which does not need to estimate any channel parameter. In this paper, the received sampled signal is transformed through multiscale wavelet to obtain a state transition equation and an observation equation based on the stationarity theory of wavelet coefficients in time domain. Then through the Kalman filter method, fractional signal of arbitrary scale is easily figured out. Finally, fractional noise interference is subtracted from the received signal. Performance analysis and computer simulations reveal that this algorithm is effective to reduce the strong fractional noise when the sampling rate is low. 12. Forecasting the Amount of Waste-Sewage Water Discharged into the Yangtze River Basin Based on the Optimal Fractional Order Grey Model. Science.gov (United States) Li, Shuliang; Meng, Wei; Xie, Yufeng 2017-12-23 With the rapid development of the Yangtze River economic belt, the amount of waste-sewage water discharged into the Yangtze River basin increases sharply year by year, which has impeded the sustainable development of the Yangtze River basin. The water security along the Yangtze River basin is very important for China, It is something aboutwater security of roughly one-third of China's population and the sustainable development of the 19 provinces, municipalities and autonomous regions among the Yangtze River basin. Therefore, a scientific prediction of the amount of waste-sewage water discharged into Yangtze River basin has a positive significance on sustainable development of industry belt along with Yangtze River basin. This paper builds the fractional DWSGM(1,1)(DWSGM(1,1) model is short for Discharge amount of Waste Sewage Grey Model for one order equation and one variable) model based on the fractional accumulating generation operator and fractional reducing operator, and calculates the optimal order of "r" by using particle swarm optimization(PSO)algorithm for solving the minimum average relative simulation error. Meanwhile, the simulation performance of DWSGM(1,1)model with the optimal fractional order is tested by comparing the simulation results of grey prediction models with different orders. Finally, the optimal fractional order DWSGM(1,1)grey model is applied to predict the amount of waste-sewage water discharged into the Yangtze River basin, and corresponding countermeasures and suggestions are put forward through analyzing and comparing the prediction results. This paper has positive significance on enriching the fractional order modeling method of the grey system. 13. Comparison of five wastewater COD fractionation methods for dynamic simulation of MBR systems. Science.gov (United States) Ruiz, Luz M; Pérez, Jorge I; Gómez, Miguel Ángel 2014-01-01 Five different wastewater COD fractionation methods were employed for simulating an experimental MBR wastewater treatment plant using WEST. The predictions of dynamic simulations using as input the data obtained according to each influent characterization methodology were compared with the results of the experimental system and differences between experimental and predicted values were analyzed in order to select the fractionation method which provides the best fitting and minimizes errors. Three of these methods were based on the determination of the biodegradable fractions using respirometric assays of real wastewater filtered through 0.45- and 0.22-μm pore size filters or adding a previous flocculation step before filtration. Moreover, a method based on physicochemical analyses and another one based on theoretical coefficients were also compared. Simulated system performance and effluent quality greatly depended upon the influent characterization and the proper model calibration. Thus the importance of selecting a suitable fractionation methodology is high, especially in MBR systems working at specific operational conditions that may alter COD fractions. In this study, MLSS in the bioreactors and sludge supernatant COD concentrations were better predicted when the influent characterization was based on respirometric methods. Both the method based on theoretical coefficients and the physicochemical method underestimated the particulate inert fraction and therefore, also the MLSS concentrations. Moreover, these results showed that for a correct effluent COD prediction in MBR systems, it is necessary to take into account that the membrane retained part of the soluble inert fraction. 14. Design of the fractional-order PIλDµ controllers based on the optimization with self-organizing migrating algorithm Directory of Open Access Journals (Sweden) Ľubomír Dorčák 2007-12-01 Full Text Available Design of fractional-order controllers based on optimization methods is one of the intensively developed trends of the present time. There are several quality control criterions to evaluate the controller performance and to design the controller parameters by optimization. All of these objective functions are almost always multimodal in this case - so they have too complex geometric surface with many local extrema. In this context the choice of the optimization method is very important. In this paper we present a synthesis method for the design of fractional-order PIλDµ controllers based on an intelligent optimization method with so called self-organizing migrating algorithm utilizing the principles of artificial intelligence. Along with the mathematical description we will present also simulation results on illustrative examples to demonstrate the advantages of this method and advantages of the fractional-order PIλDµ controllers in comparison with traditional PID controllers. 15. A higher order numerical method for time fractional partial differential equations with nonsmooth data Science.gov (United States) Xing, Yanyuan; Yan, Yubin 2018-03-01 Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results. 16. Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem Directory of Open Access Journals (Sweden) Min Jia 2012-01-01 Full Text Available We study a model arising from porous media, electromagnetic, and signal processing of wireless communication system -tαx(t=f(t,x(t,x'(t,x”(t,…,x(n-2(t, 0fractional differential equation are obtained. Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method. 17. A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel Science.gov (United States) Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F. 2018-02-01 A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied. 18. Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System Directory of Open Access Journals (Sweden) Chen Yuming 2011-01-01 Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility. 19. Single image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction. Science.gov (United States) Yang, Qi; Zhang, Yanzhu; Zhao, Tiebiao; Chen, YangQuan 2017-04-04 Image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction aims to recover detailed information from low-resolution images and reconstruct them into high-resolution images. Due to the limited amount of data and information retrieved from low-resolution images, it is difficult to restore clear, artifact-free images, while still preserving enough structure of the image such as the texture. This paper presents a new single image super-resolution method which is based on adaptive fractional-order gradient interpolation and reconstruction. The interpolated image gradient via optimal fractional-order gradient is first constructed according to the image similarity and afterwards the minimum energy function is employed to reconstruct the final high-resolution image. Fractional-order gradient based interpolation methods provide an additional degree of freedom which helps optimize the implementation quality due to the fact that an extra free parameter α-order is being used. The proposed method is able to produce a rich texture detail while still being able to maintain structural similarity even under large zoom conditions. Experimental results show that the proposed method performs better than current single image super-resolution techniques. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved. 20. Complex systems fractionality, time-delay and synchronization CERN Document Server Sun, Jian-Qiao 2012-01-01 "Complex Systems: Fractionality, Time-delay and Synchronization" covers the most recent developments and advances in the theory and application of complex systems in these areas. Each chapter was written by scientists highly active in the field of complex systems. The book discusses a new treatise on fractional dynamics and control, as well as the new methods for differential delay systems and control. Lastly, a theoretical framework for the complexity and synchronization of complex system is presented. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. It can also serve as a reference book for graduate students in physics, applied mathematics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Jian-Qiao Sun is a Professor at the University of California, Merced, USA. 1. Research of digital constant fraction discriminator in PET system International Nuclear Information System (INIS) Du Yaoyao; Hu Xuanhou; Wu Jianping; Wang Peilin; Li Xiaohui; Li Daowu; Li Ke; Wei Long 2012-01-01 The research on digital constant fraction discriminator of spike pulse signal in PET detector is introduced. Based on FPGA technique, rapid signal's time information is extracted via DCFD algorithm after a high-speed ADC digitization. Experiment results show that time resolution of DCFD is 772 ps, which meets the requirement of time measurement in PET system well. (authors) 2. Existence of solutions to singular fractional differential systems with impulses Directory of Open Access Journals (Sweden) Xingyuan Liu 2012-11-01 Full Text Available By constructing a weighted Banach space and a completely continuous operator, we establish the existence of solutions for singular fractional differential systems with impulses. Our results are proved using the Leray-Schauder nonlinear alternative, and are illustrated with examples. 3. Adaptive two-degree-of-freedom PI for speed control of permanent magnet synchronous motor based on fractional order GPC. Science.gov (United States) Qiao, Wenjun; Tang, Xiaoqi; Zheng, Shiqi; Xie, Yuanlong; Song, Bao 2016-09-01 In this paper, an adaptive two-degree-of-freedom (2Dof) proportional-integral (PI) controller is proposed for the speed control of permanent magnet synchronous motor (PMSM). Firstly, an enhanced just-in-time learning technique consisting of two novel searching engines is presented to identify the model of the speed control system in a real-time manner. Secondly, a general formula is given to predict the future speed reference which is unavailable at the interval of two bus-communication cycles. Thirdly, the fractional order generalized predictive control (FOGPC) is introduced to improve the control performance of the servo drive system. Based on the identified model parameters and predicted speed reference, the optimal control law of FOGPC is derived. Finally, the designed 2Dof PI controller is auto-tuned by matching with the optimal control law. Simulations and real-time experimental results on the servo drive system of PMSM are provided to illustrate the effectiveness of the proposed strategy. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved. 4. Systemic sclerosis, birth order and parity. Science.gov (United States) Russo, Paul A J; Lester, Susan; Roberts-Thomson, Peter J 2014-06-01 A recent study identified increasing birth order to be a risk factor for the development of systemic sclerosis (SSc). This finding supports the theory that transplacental microchimerism may be a key pathological event in the initiation of SSc. We investigated the relationship between birth order and parity and the age of onset of SSc in South Australia. A retrospective analysis of patient data in the South Australian Scleroderma Register was performed. Data were obtained from a mailed questionnaire. Control data was collected prospectively using a similar questionnaire. The relationship between birth order, family size or parity and risk of subsequent development of SSc was analyzed by mixed effects logistic regression analysis. Three hundred and eighty-seven index probands were identified and compared with 457 controls. Controls were well matched for gender, but not for age. No statistically significant relationship was identified between SSc and birth order, parity in females, family size, age at first pregnancy in females or gender of first child in parous females. Our data suggests that parity, age at first pregnancy and the gender of the first child are not relevant factors in our understanding of the epidemiology and pathogenesis of SSc. Birth order and family size in both genders also appears irrelevant. These results argue against microchimerism as being relevant in the pathogenesis of SSc and add further support to the theory that stochastic events may be important in the etiopathogenesis of SSc. © 2013 Asia Pacific League of Associations for Rheumatology and Wiley Publishing Asia Pty Ltd. 5. On the Existence of Locally Attractive Solutions of a Nonlinear Quadratic Volterra Integral Equation of Fractional Order Directory of Open Access Journals (Sweden) Abbas MohamedI 2010-01-01 Full Text Available The authors employs a hybrid fixed point theorem involving the multiplication of two operators for proving an existence result of locally attractive solutions of a nonlinear quadratic Volterra integral equation of fractional (arbitrary order. Investigations will be carried out in the Banach space of real functions which are defined, continuous, and bounded on the real half axis . 6. A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions Directory of Open Access Journals (Sweden) Bashir Ahmad 2013-01-01 Full Text Available We develop the existence theory for nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type boundary conditions involving nonintersecting finite many strips of arbitrary length. Our results are based on some standard tools of fixed point theory. For the illustration of the results, some examples are also discussed. 7. System analysis of optimum fractionation of high level liquid radwaste International Nuclear Information System (INIS) Gotovchikov, V.T.; Kuzin, R.E.; Logunov, M.V. 2012-01-01 One of the key stages of a closed nuclear fuel cycle is fractionating of high-level waste with its subsequent solidification. The initial raw product for fractionating is condensed liquid radwaste of high specific activity levels (water tailing solutions) generated by the PUREX process. The system analysis of the problem is described in the article. A series of factors that determine the complexity and importance of high-level liquid radwaste fractionating are presented. The hypothesis with the suggestion to view nuclear transmutation as a means of reducing overall activity levels of long-lived nuclides both by burning a number of fissionable nuclides in specially-built reactors, and by conversion of other long-lived nuclides into short-lived by exposing them in an accelerator is discussed [ru 8. Fractional exclusion statistics in systems with localized states International Nuclear Information System (INIS) Nemnes, G A; Anghel, D V 2013-01-01 We develop a model based on the fractional exclusion statistics to describe systems with localized states. The local distribution of the energy levels is captured in the formalism by including the positions in the definition of the species. The particle distributions on the energy axis, as well as in the real space are determined for test-case systems with a peak/dip profile in the local density of states. 9. Global Uniqueness Results for Fractional Order Partial Hyperbolic Functional Differential Equations Directory of Open Access Journals (Sweden) Benchohra Mouffak 2011-01-01 Full Text Available Abstract We investigate the global existence and uniqueness of solutions for some classes of partial hyperbolic differential equations involving the Caputo fractional derivative with finite and infinite delays. The existence results are obtained by applying some suitable fixed point theorems. 10. Calculation of multicomponent compound properties using generalization of thermodynamics in derivatives of fractional order International Nuclear Information System (INIS) Magomedov, R A; Meilanov, R P; Akhmedov, E N; Aliverdiev, A A 2016-01-01 The generalization of thermodynamics in formalism of fractional derivatives is presented. One-parametric “fractal” state equation with second virial coefficient is obtained. The calculation of entropy S and compressibility z of the refrigerant freon R409B for the pressure range from 0.01 to 3.8 MPa and temperature range from 210 to 370 K is given. (paper) 11. A (star)-BASED MINKOWSKI'S INEQUALITY FOR SUGENO FRACTIONAL INTEGRAL OF ORDER alpha > 0 Czech Academy of Sciences Publication Activity Database Babkhani, A.; Agahi, H.; Mesiar, Radko 2015-01-01 Roč. 18, č. 4 (2015), s. 862-874 ISSN 1311-0454 Institutional support: RVO:67985556 Keywords : fuzzy integral * Sugeno fractional integral * Minkowski's inequality Subject RIV: BA - General Mathematics Impact factor: 2.246, year: 2015 http://library.utia.cas.cz/separaty/2015/E/mesiar-0446629.pdf 12. What fraction of white dwarfs are members of binary systems? International Nuclear Information System (INIS) Holberg, J B 2009-01-01 White dwarfs were originally discovered as the subordinate faint companions of bright nearby stars (i.e. Sirius B and 40 Eri B). Several general categories of binary systems involving white dwarfs are recognized: Sirius-like systems, where the white dwarf may be difficult to detect, binary systems containing white dwarfs and low mass stars, where the white dwarf is often readily discerned; and double degenerate systems. Different modes of white dwarf discovery influence our perception of both the overall binary fraction and the nature of these systems; proper motion surveys emphasize resolved systems, while photometric surveys emphasize unresolved systems containing relatively hot white dwarfs. Recent studies of the local white dwarf population offer some hope of achieving realistic estimates of the relative number of binary systems containing white dwarfs. A sample of 132 white dwarfs within 20 pc indicates that an individual white dwarf has a probability of 32 ± 8% of occurring within a binary or multiple star system. 13. Series-, Parallel-, and Inter-Connection of Solid-State Arbitrary Fractional-Order Capacitors: Theoretical Study and Experimental Verification KAUST Repository Kartci, Aslihan 2018-02-26 In the paper, general analytical formulas are introduced for the determination of equivalent impedance, magnitude, and phase, i.e. order, for n arbitrary fractional-order capacitors (FoCs) connected in series, parallel, and their interconnection. The approach presented helps to evaluate these relevant quantities in the fractional domain since the order of each element has a significant effect on the impedance of each FoC and their equivalent capacitance cannot be considered. Three types of solid-state fractional-order passive capacitors of different orders, using ferroelectric polymer and reduced Graphene Oxide-percolated P(VDF-TrFE-CFE) composite structures, are fabricated and characterized. Using an impedance analyzer, the behavior of the devices was found to be stable in the frequency range 0.2MHz–20MHz, with a phase angle deviation of ±4 degrees. Multiple numerical and experimental case studies are given, in particular for two and three connected FoCs. The fundamental issues of the measurement units of the FoCs connected in series and parallel are derived. A MATLAB open access source code is given in Appendix sec:append for easy calculation of the equivalent FoC magnitude and phase. The experimental results are in good agreement with the theoretical assumptions. 14. The fractional virial potential energy in two-component systems Directory of Open Access Journals (Sweden) Caimmi R. 2008-01-01 Full Text Available Two-component systems are conceived as macrogases, and the related equation of state is expressed using the virial theorem for subsystems, under the restriction of homeoidally striated density profiles. Explicit calculations are performed for a useful reference case and a few cases of astrophysical interest, both with and without truncation radius. Shallower density profiles are found to yield an equation of state, φ = φ(y, m, characterized (for assigned values of the fractional mass, m = Mj /Mi by the occurrence of two extremum points, a minimum and a maximum, as found in an earlier attempt. Steeper density profiles produce a similar equation of state, which implies that a special value of m is related to a critical curve where the above mentioned extremum points reduce to a single horizontal inflexion point, and curves below the critical one show no extremum points. The similarity of the isofractional mass curves to van der Waals' isothermal curves, suggests the possibility of a phase transition in a bell-shaped region of the (Oyφ plane, where the fractional truncation radius along a selected direction is y = Rj /Ri , and the fractional virial potential energy is φ = (Eji vir /(Eij vir . Further investigation is devoted to mass distributions described by Hernquist (1990 density profiles, for which an additional relation can be used to represent a sample of N = 16 elliptical galaxies (EGs on the (Oyφ plane. Even if the evolution of elliptical galaxies and their hosting dark matter (DM haloes, in the light of the model, has been characterized by equal fractional mass, m, and equal scaled truncation radius, or concentration, Ξu = Ru /r† , u = i, j, still it cannot be considered as strictly homologous, due to different values of fractional truncation radii, y, or fractional scaling radii, y† = r† /r† , deduced from sample objects. 15. Development of magnetic order in superconducting systems International Nuclear Information System (INIS) Moncton, D.E.; Shirane, G.; Thomlinson, W. 1979-08-01 Two different classes of rare-earth (RE) ternary superconductors (RERh 4 B 4 and REMo 6 S 8 , X=S, Se) have provided the first instances in which chemically ordered sublattices of magnetic ions exist in superconductors. Neutron scattering studies show that simple, conventional antiferromagnetism coexists with superconductivity in a number of systems, while destruction of superconductivity occurs with the onset of ferromagnetism. The magnetic structural details are summarized for the coexistent antiferromagnets, and review measurements on the superconducting → ferromagnetic transition in ErRh 4 B 4 16. A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part I: Model development and observability analysis Science.gov (United States) Li, Xiaoyu; Fan, Guodong; Pan, Ke; Wei, Guo; Zhu, Chunbo; Rizzoni, Giorgio; Canova, Marcello 2017-11-01 The design of a lumped parameter battery model preserving physical meaning is especially desired by the automotive researchers and engineers due to the strong demand for battery system control, estimation, diagnosis and prognostics. In light of this, a novel simplified fractional order electrochemical model is developed for electric vehicle (EV) applications in this paper. In the model, a general fractional order transfer function is designed for the solid phase lithium ion diffusion approximation. The dynamic characteristics of the electrolyte concentration overpotential are approximated by a first-order resistance-capacitor transfer function in the electrolyte phase. The Ohmic resistances and electrochemical reaction kinetics resistance are simplified to a lumped Ohmic resistance parameter. Overall, the number of model parameters is reduced from 30 to 9, yet the accuracy of the model is still guaranteed. In order to address the dynamics of phase-change phenomenon in the active particle during charging and discharging, variable solid-state diffusivity is taken into consideration in the model. Also, the observability of the model is analyzed on two types of lithium ion batteries subsequently. Results show the fractional order model with variable solid-state diffusivity agrees very well with experimental data at various current input conditions and is suitable for electric vehicle applications. 17. On the analysis of chemical kinetics system pertaining to a fractional derivative with Mittag-Leffler type kernel. Science.gov (United States) Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru 2017-10-01 The pivotal aim of this paper was to analyze a new fractional model of chemical kinetics system related to a newly discovered Atangana-Baleanu derivative with fractional order having non-singular and non-local kernel. The numerical solution is derived by making use of the iterative scheme. The existence of the solution of chemical kinetics system of arbitrary order is examined by implementing the fixed-point theorem. The uniqueness of the special solution of the studied model is shown. The effect of different variables and order of arbitrary ordered derivative on concentrations is demonstrated in tabular and graphical forms. The numerical results for chemical kinetics system pertaining to the newly derivative with fractional order are compared with the chemical kinetics system involving classical derivative. 18. FRACTIONAL CRYSTALLIZATION TESTING WITH INTERIM PRETREATMENT SYSTEM FEEDS International Nuclear Information System (INIS) HERTING DL 2008-01-01 The fractional crystallization process was developed as a pretreatment method for saltcake waste retrieved from Hanford single-shell tanks (SST). The process separates the retrieved SST waste into a high-level waste stream containing the bulk of the radionuclides and a low-activity waste stream containing the bulk of the nonradioactive sodium salts. The Interim Pretreatment System project shifted the focus on pretreatment planning from SST waste to double-shell tank waste 19. Peripheral arterial disease screening for hemodialysis patients using a fractional-order integrator and transition probability decision-making model. Science.gov (United States) Wu, Jian-Xing; Li, Chien-Ming; Chen, Guan-Chun; Ho, Yueh-Ren; Lin, Chia-Hung 2017-04-01 Atherosclerosis and resultant peripheral arterial disease (PAD) are common complications in patients with type 2 diabetes mellitus or end-stage renal disease and in elderly patients. The prevalence of PAD is higher in patients receiving haemodialysis therapy. For early assessment of arterial occlusion using bilateral photoplethysmography (PPG), such as changes in pulse transit time and pulse shape, bilateral timing differences could be used to identify the risk level of PAD. Hence, the authors propose a discrete fractional-order integrator to calculate the bilateral area under the systolic peak (AUSP). These indices indicated the differences in both rise-timing and amplitudes of PPG signals. The dexter and sinister AUSP ratios were preliminarily used to separate the normal condition from low/high risk of PAD. Then, transition probability-based decision-making model was employed to evaluate the risk levels. The joint probability could be specified as a critical threshold, < 0.81, to identify the true positive for screening low or high risk level of PAD, referring to the patients' health records. In contrast to the bilateral timing differences and traditional methods, the proposed model showed better efficiency in PAD assessments and provided a promising strategy to be implemented in an embedded system. 20. Variable-order fractional MSD function to describe the evolution of protein lateral diffusion ability in cell membranes Science.gov (United States) Yin, Deshun; Qu, Pengfei 2018-02-01 Protein lateral diffusion is considered anomalous in the plasma membrane. And this diffusion is related to membrane microstructure. In order to better describe the property of protein lateral diffusion and find out the inner relationship between protein lateral diffusion and membrane microstructure, this article applies variable-order fractional mean square displacement (f-MSD) function for characterizing the anomalous diffusion. It is found that the variable order can reflect the evolution of diffusion ability. The results of numerical simulation demonstrate variable-order f-MSD function can predict the tendency of anomalous diffusion during the process of confined diffusion. It is also noted that protein lateral diffusion ability during the processes of confined and hop diffusion can be split into three parts. In addition, the comparative analyses reveal that the variable order is related to the confinement-domain size and microstructure of compartment boundary too. 1. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise Science.gov (United States) Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao 2016-08-01 The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative. 2. Modeling vehicle operating speed on urban roads in Montreal: a panel mixed ordered probit fractional split model. Science.gov (United States) Eluru, Naveen; Chakour, Vincent; Chamberlain, Morgan; Miranda-Moreno, Luis F 2013-10-01 Vehicle operating speed measured on roadways is a critical component for a host of analysis in the transportation field including transportation safety, traffic flow modeling, roadway geometric design, vehicle emissions modeling, and road user route decisions. The current research effort contributes to the literature on examining vehicle speed on urban roads methodologically and substantively. In terms of methodology, we formulate a new econometric model framework for examining speed profiles. The proposed model is an ordered response formulation of a fractional split model. The ordered nature of the speed variable allows us to propose an ordered variant of the fractional split model in the literature. The proposed formulation allows us to model the proportion of vehicles traveling in each speed interval for the entire segment of roadway. We extend the model to allow the influence of exogenous variables to vary across the population. Further, we develop a panel mixed version of the fractional split model to account for the influence of site-specific unobserved effects. The paper contributes substantively by estimating the proposed model using a unique dataset from Montreal consisting of weekly speed data (collected in hourly intervals) for about 50 local roads and 70 arterial roads. We estimate separate models for local roads and arterial roads. The model estimation exercise considers a whole host of variables including geometric design attributes, roadway attributes, traffic characteristics and environmental factors. The model results highlight the role of various street characteristics including number of lanes, presence of parking, presence of sidewalks, vertical grade, and bicycle route on vehicle speed proportions. The results also highlight the presence of site-specific unobserved effects influencing the speed distribution. The parameters from the modeling exercise are validated using a hold-out sample not considered for model estimation. The results indicate 3. Modulating Functions Based Algorithm for the Estimation of the Coefficients and Differentiation Order for a Space-Fractional Advection-Dispersion Equation KAUST Repository Aldoghaither, Abeer 2015-12-01 In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton\\'s iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations. 4. Integrated Fractional Load and Packet Scheduling for OFDMA Systems DEFF Research Database (Denmark) Monghal, Guillaume Damien; Kumar, S.; Pedersen, Klaus I. 2009-01-01 . This type of situation should result in a global increase of signal to interference and noise ratio (SINR) conditions in the network. We propose different methods integrating the transmission pattern selection to the packet scheduling functionality of the enode-B depending only on the channel quality...... indicator (CQI) reports from the user equipments. Fractional load handling is operated without inter eNode-B coordination. We conclude that the system can operate under fractional load conditions if the CQI is calculated with wideband interference. Further gain can be obtained if the CQI is calculated...... with local interference, however, in that case, it is necessary to inject a certain time correlation in the transmission patterns due to reporting delay.... 5. Two-temperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer International Nuclear Information System (INIS) Ezzat, Magdy A.; El-Karamany, Ahmed S.; Ezzat, Shereen M. 2012-01-01 Highlights: ► We model fractional order dual-phase-lag heat conduction law. ► We applied the model on a perfect conducting half-space of elastic material. ► Some theories of generalized thermoelasticity follow as limit cases. ► State space approach is adopted for the solution of one-dimensional problems. ► The model will improve the efficiency of thermoelectric material. - Abstract: A new mathematical model of two-temperature magneto-thermoelasticity is constructed where the fractional order dual-phase-lag heat conduction law is considered. The state space approach developed in Ezzat (2008) is adopted for the solution of one-dimensional application for a perfect conducting half-space of elastic material, which is thermally shocked in the presence of a transverse magnetic field. The Laplace transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some theories of generalized thermoelasticity follow as limit cases. Some comparisons have been shown in figures to estimate effects of temperature discrepancy and fractional order parameter on all the studied fields. 6. Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator Science.gov (United States) Owolabi, Kolade M. 2018-03-01 In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus. 7. Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations KAUST Repository Jin, Bangti 2013-01-01 We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics. 8. Local Fractional Operator for a One-Dimensional Coupled Burger Equation of Non-Integer Time Order Parameter Directory of Open Access Journals (Sweden) Sunday O. Edeki 2018-03-01 Full Text Available In this study, approximate solutions of a system of time-fractional coupled Burger equations were obtained by means of a local fractional operator (LFO in the sense of the Caputo derivative. The LFO technique was built on the basis of the standard differential transform method (DTM. Illustrative examples used in demonstrating the effectiveness and robustness of the proposed method show that the solution method is very efficient and reliable as – unlike the variational iteration method – it does not depend on any process of identifying Lagrange multipliers, even while still maintaining accuracy. 9. Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems International Nuclear Information System (INIS) Owolabi, Kolade M. 2016-01-01 The aim of this paper is to examine pattern formation in the sub— and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order α, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions. 10. The Fractional Virial Potential Energy in Two-Component Systems Directory of Open Access Journals (Sweden) Caimmi, R. 2008-12-01 Full Text Available Two-component systems are conceived as macrogases, and the related equation of state is expressed using the virial theorem for subsystems, under the restriction of homeoidally striated density profiles. Explicit calculations are performed for a useful reference case and a few cases of astrophysical interest, both with and without truncation radius. Shallower density profiles are found to yield an equation of state,phi=phi(y,m$, characterized (for assigned values of the fractional mass,$m=M_j/ M_i$by the occurrence of two extremum points, a minimum and a maximum, as found in an earlier attempt. Steeper density profiles produce a similar equation of state, which implies that a special value of$m$is related to a critical curve where the above mentioned extremum points reduce to a single horizontal inflexion point, and curves below the critical one show no extremum points. The similarity of the isofractional mass curves to van der Waals' isothermal curves, suggests the possibility of a phase transition in a bell-shaped region of the$({sf O}yphi$plane, where the fractional truncation radius along a selected direction is$y=R_j/R_i$, and the fractional virial potential energy is$phi=(E_{ji}_mathrm{vir}/(E_{ij}_mathrm{vir}$. Further investigation is devoted to mass distributions described by Hernquist (1990 density profiles, for which an additional relation can be used to represent a sample of$N=16$elliptical galaxies (EGs on the$({sf O}yphi$plane. Even if the evolution of elliptical galaxies and their hosting dark matter (DM haloes, in the light of the model, has been characterized by equal fractional mass,$m$, and equal scaled truncation radius, or concentration,$Xi_u=R_u/r_u^dagger$,$u=i,j$, still it cannot be considered as strictly homologous, due to different values of fractional truncation radii,$y$, or fractional scaling radii,$y^dagger=r_j^dagger/r_i^dagger$, deduced from sample objects. 11. Silicon Isotopic Fractionation in a Tropical Soil-Plant System Science.gov (United States) Opfergelt, S.; Delstanche, S.; Cardinal, D.; Andre, L.; Delvaux, B. 2006-12-01 Silica fluxes to soil solutions and water streams are controlled by both abiotic and biotic processes occurring in a Si soil-plant cycle that can be significant in comparison with Si weathering input and hydrological output. The quantification of Si-isotopic fractionation by these processes is highly promising to study the Si soil-plant cycle. Therein, the fate of aqueous monosilicic acid H4SiO4, as produced by silicate weathering, may take four paths: (1) uptake by plants and recycling through falling litter, (2) formation of clay minerals, (3) specific adsorption onto Al and Fe oxides, (4) leaching in drainage waters and export from watersheds. Here we report on detailed Si-isotopic compositions of various Si pools in a tropical soil-plant system involving old stands of banana (Musa acuminata Colla, cv Grande Naine) cropped on a weathering sequence of soils derived from andesitic volcanic ash and pumice deposits in Cameroon, West Africa. Si-isotopic compositions were measured by MC-ICP-MS in dry plasma mode with external Mg doping with a reproducibility of 0.08 permil (2stdev). Results were expressed as delta29Si vs NBS28. The compositions were determined in plant parts, bulk soils, clay fractions (less than 2um) and stream waters used for crop irrigation. Of the weathering sequence, we selected young (Y) and old (O) volcanic soils (vs). Yvs are rich in weatherable minerals, and contain large amounts of pumice gravels; their clay fraction (10-35 percent) contains allophane, halloysite and ferrihydrite. Oppositely, Ovs are strongly weathered and fine clayey soils (75-96 percent clay) rich in halloysite, kaolinite, gibbsite and goethite. Intra-plant fractionation between roots and shoots and within shoots confirmed our previous data measured on banana plants grown in hydroponics. The bulk plant isotopic composition was heavier at Ovs than at Yvs giving a fractionation factor per atomic mass unit between plants and their irrigation water Si source (+0.61 permil) of 12. The fractional calculus theory and applications of differentiation and integration to arbitrary order CERN Document Server Oldham, Keith B 1974-01-01 In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat 13. Distributed order reaction-diffusion systems associated with Caputo derivatives Science.gov (United States) Saxena, R. K.; Mathai, A. M.; Haubold, H. J. 2014-08-01 This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables 14. On Attractivity and Positivity of Solutions for Functional Integral Equations of Fractional Order Directory of Open Access Journals (Sweden) Xianyong Huang 2013-01-01 order given by x(t=q(t+f1(t,x(α1(t,x(α2(t+(f2(t,x(β1(t,x(β2(t/Γ(α×∫0t(t−sα−1f3(t,s,x(γ1(s, x(γ2(sds: sufficient conditions for the existence, global attractivity, and ultimate positivity of solutions of the equations are derived. The main tools include the techniques of measures of noncompactness and a recent measure theoretic fixed point theorem of Dhage. Our investigations are placed in the Banach space of continuous and bounded real-valued functions defined on unbounded intervals. Moreover, two examples are given to illustrate our results. 15. Conservation laws for certain time fractional nonlinear systems of partial differential equations Science.gov (United States) Singla, Komal; Gupta, R. K. 2017-12-01 In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems. 16. Skinner-Rusk unified formalism for higher-order systems Science.gov (United States) Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso 2012-07-01 The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, first-order and higher-order field theories, and higher-order autonomous systems. In this work we present a generalization of this formalism for higher-order non-autonomous mechanical systems. 17. On the evaluation of modified Bessel functions of the second kind and fractional order for synchrotron radiation calculations International Nuclear Information System (INIS) Rutt, H.N. 2003-01-01 The modified Bessel functions of the second kind and fractional order K 1/3 (x) and K 2/3 (x) are of importance in the calculation of the frequency spectrum of synchrotron radiation. The parameter range of interest is typically 10 -6 x10. Recently, there has been particular interest in the generation of 'terahertz' radiation, which can be coherently enhanced by many orders of magnitude when the electron bunch length is shorter than the terahertz wavelength. This requires evaluation of the Bessel functions for small values of the argument. It is shown that the series commonly used to evaluate these functions has poor convergence properties under these conditions. An alternative series is derived which has much better convergence for x1 18. A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation Science.gov (United States) Tayebi, A.; Shekari, Y.; Heydari, M. H. 2017-07-01 Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena. 19. Organic matter fractions in areas Oxisol under different management systems in Cerrado the State of Goiás, Brazil Directory of Open Access Journals (Sweden) Roni Fernandes Guareschi 2013-12-01 Full Text Available The objective of this study was to evaluate the physical and chemical fractions of soil organic matter (SOM, as well as perform the spectroscopic analysis in ultraviolet-visible humic acid in a Oxisol under no-tillage system (NTS with different years of implementation, and compare them to areas of native cerrado and pasture. Was evaluated five areas namely: native cerrado (CE, planted pasture (PA with Brachiaria decumbens; NTS with 3 (NTS 3 years of implementation; NTS with 15 years (NTS 15 of implementation and NTS with more than 20 (NTS 20 years of implementation. The levels and total carbon stocks and humic fractions of SOM, increased with deployment time the NTS at all depths analyzed, with the humic fractions presented the following order: fraction fulvic acid > fraction humic acid > humin fraction. The results showed that depending on the time of implementation of the NTS was observed an increase of more stable fractions of humic substances and physical fractions of SOM, providing greater stability of this system. There is increasing the E4/E6 ratio of humic acids according on the time of implementation of the NTS, demonstrating an increase of aliphatic structures. The area evaluated PA had the lowest concentrations and inventories of humic fractions, carbon associated with minerals (CAM and E4/E6 ratio, demonstrating to be in an advanced stage of degradation relative to the other areas assessed. 20. EVOLUTION OF THE BINARY FRACTION IN DENSE STELLAR SYSTEMS International Nuclear Information System (INIS) Fregeau, John M.; Ivanova, Natalia; Rasio, Frederic A. 2009-01-01 Using our recently improved Monte Carlo evolution code, we study the evolution of the binary fraction in globular clusters. In agreement with previous N-body simulations, we find generally that the hard binary fraction in the core tends to increase with time over a range of initial cluster central densities for initial binary fractions ∼<90%. The dominant processes driving the evolution of the core binary fraction are mass segregation of binaries into the cluster core and preferential destruction of binaries there. On a global scale, these effects and the preferential tidal stripping of single stars tend to roughly balance, leading to overall cluster binary fractions that are roughly constant with time. Our findings suggest that the current hard binary fraction near the half-mass radius is a good indicator of the hard primordial binary fraction. However, the relationship between the true binary fraction and the fraction of main-sequence stars in binaries (which is typically what observers measure) is nonlinear and rather complicated. We also consider the importance of soft binaries, which not only modify the evolution of the binary fraction, but can also drastically change the evolution of the cluster as a whole. Finally, we briefly describe the recent addition of single and binary stellar evolution to our cluster evolution code. 1. Ordered Organic Systems and Molecular Rectifiers Science.gov (United States) 1975-03-31 produced films of manganese stearate (abbr., MnSt ?) by the Langmuir-Blodgett technique. We find that they can be prepared in multilayers. In our...the sample. We also prepared .large quantities of crystalline MnSt ? powder and studied this compound by other means. We verified that the MnSt ...ESR spectrometer so Uiat we can observe single monolayers of MnSt , In order to test whether the magnetic transition persists In a truly two-dimen 2. Superintegrable systems with third-order integrals of motion Energy Technology Data Exchange (ETDEWEB) Marquette, Ian [Departement de physique et Centre de recherche mathematiques, Universite de Montreal, CP 6128, Succursale Centre-Ville, Montreal, Quebec H3C 3J7 (Canada); Winternitz, Pavel [Departement de mathematiques et de statistique et Centre de recherche mathematiques, Universite de Montreal, CP 6128, Succursale Centre-Ville, Montreal, Quebec H3C 3J7 (Canada)], E-mail: ian.marquette@umontreal.ca, E-mail: wintern@CRM.UMontreal.CA 2008-08-01 Two-dimensional superintegrable systems with one third-order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is stressed. New results on the use of classical and quantum third-order integrals are presented in sections 5 and 6. 3. Calcium isotope fractionation in a silicate dominated Cenozoic aquifer system Science.gov (United States) Li, Junxia; DePaolo, Donald J.; Wang, Yanxin; Xie, Xianjun 2018-04-01 To understand the characteristics of Ca isotope composition and fractionation in silicate-dominated Quaternary aquifer system, hydrochemical and isotope studies (87Sr/86Sr, 13CDIC and 44/40Ca) were conducted on groundwater, sediment and rock samples from the Datong basin, China. Along the groundwater flow path from the basin margin to the center, groundwater hydrochemical type evolves from Ca-HCO3 to Na-HCO3/Na-Cl type, which results from aluminosilicate hydrolysis, vertical mixing, cation exchange between CaX2 and NaX, and calcite/dolomite precipitation. These processes cause the decrease in groundwater Ca concentration and the associated modest fractionation of groundwater Ca isotopes along the flowpath. The groundwater δ44/40Ca value varies from -0.11 to 0.49‰. The elevated δ44/40Ca ratios in shallow groundwater are attributed to vertical mixing involving addition of irrigation water, which had the average δ44/40Ca ratio of 0.595‰. Chemical weathering of silicate minerals and carbonate generates depleted δ44/40Ca signatures in groundwater from Heng Mountain (east area) and Huanghua Uplift (west area), respectively. Along the groundwater flow path from Heng Mountain to central area of east area, cation exchange between CaX2 and NaX on clay mineral results in the enrichment of heavier Ca isotope in groundwater. All groundwater samples are oversaturated with respect to calcite and dolomite. The groundwater environment rich in organic matter promotes the precipitation of carbonate minerals via the biodegradation of organic carbon, thereby further promoting the elevation of groundwater δ44/40Ca ratios. 4. Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form Directory of Open Access Journals (Sweden) Sifeu Takougang Kingni 2017-01-01 Full Text Available A linear resistive-capacitive-inductance shunted junction (LRCLSJ model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system. 5. Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays. Science.gov (United States) Peng, Xiao; Wu, Huaiqin; Song, Ka; Shi, Jiaxin 2017-10-01 This paper is concerned with the global Mittag-Leffler synchronization and the synchronization in finite time for fractional-order neural networks (FNNs) with discontinuous activations and time delays. Firstly, the properties with respect to Mittag-Leffler convergence and convergence in finite time, which play a critical role in the investigation of the global synchronization of FNNs, are developed, respectively. Secondly, the novel state-feedback controller, which includes time delays and discontinuous factors, is designed to realize the synchronization goal. By applying the fractional differential inclusion theory, inequality analysis technique and the proposed convergence properties, the sufficient conditions to achieve the global Mittag-Leffler synchronization and the synchronization in finite time are addressed in terms of linear matrix inequalities (LMIs). In addition, the upper bound of the setting time of the global synchronization in finite time is explicitly evaluated. Finally, two examples are given to demonstrate the validity of the proposed design method and theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved. 6. Scalable fractionation of iron oxide nanoparticles using a CO2 gas-expanded liquid system International Nuclear Information System (INIS) Vengsarkar, Pranav S.; Xu, Rui; Roberts, Christopher B. 2015-01-01 Iron oxide nanoparticles exhibit highly size-dependent physicochemical properties that are important in applications such as catalysis and environmental remediation. In order for these size-dependent properties to be effectively harnessed for industrial applications scalable and cost-effective techniques for size-controlled synthesis or size separation must be developed. The synthesis of monodisperse iron oxide nanoparticles can be a prohibitively expensive process on a large scale. An alternative involves the use of inexpensive synthesis procedures followed by a size-selective processing technique. While there are many techniques available to fractionate nanoparticles, many of the techniques are unable to efficiently fractionate iron oxide nanoparticles in a scalable and inexpensive manner. A scalable apparatus capable of fractionating large quantities of iron oxide nanoparticles into distinct fractions of different sizes and size distributions has been developed. Polydisperse iron oxide nanoparticles (2–20 nm) coated with oleic acid used in this study were synthesized using a simple and inexpensive version of the popular coprecipitation technique. This apparatus uses hexane as a CO 2 gas-expanded liquid to controllably precipitate nanoparticles inside a 1L high-pressure reactor. This paper demonstrates the operation of this new apparatus and for the first time shows the successful fractionation results on a system of metal oxide nanoparticles, with initial nanoparticle concentrations in the gram-scale. The analysis of the obtained fractions was performed using transmission electron microscopy and dynamic light scattering. The use of this simple apparatus provides a pathway to separate large quantities of iron oxide nanoparticles based upon their size for use in various industrial applications. 7. Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H − s , 0 ≤ s ≤ 1 KAUST Repository Jin, Bangti 2013-01-01 We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that Ω ⊂ ℝd , d = 1,2,3 is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in L2- and H1-norms for initial data in H-s (Ω), 0 ≤ s ≤ 1. We confirm our theoretical findings with a number of numerical tests that include initial data v being a Dirac δ-function supported on a (d-1)-dimensional manifold. © 2013 Springer-Verlag. 8. Higher-order singular value decomposition-based discrete fractional random transform for simultaneous compression and encryption of video images Science.gov (United States) Wang, Qingzhu; Chen, Xiaoming; Zhu, Yihai 2017-09-01 Existing image compression and encryption methods have several shortcomings: they have low reconstruction accuracy and are unsuitable for three-dimensional (3D) images. To overcome these limitations, this paper proposes a tensor-based approach adopting tensor compressive sensing and tensor discrete fractional random transform (TDFRT). The source video images are measured by three key-controlled sensing matrices. Subsequently, the resulting tensor image is further encrypted using 3D cat map and the proposed TDFRT, which is based on higher-order singular value decomposition. A multiway projection algorithm is designed to reconstruct the video images. The proposed algorithm can greatly reduce the data volume and improve the efficiency of the data transmission and key distribution. The simulation results validate the good compression performance, efficiency, and security of the proposed algorithm. 9. Iterative solution of high order compact systems Energy Technology Data Exchange (ETDEWEB) Spotz, W.F.; Carey, G.F. [Univ. of Texas, Austin, TX (United States) 1996-12-31 We have recently developed a class of finite difference methods which provide higher accuracy and greater stability than standard central or upwind difference methods, but still reside on a compact patch of grid cells. In the present study we investigate the performance of several gradient-type iterative methods for solving the associated sparse systems. Both serial and parallel performance studies have been made. Representative examples are taken from elliptic PDEs for diffusion, convection-diffusion, and viscous flow applications. 10. Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays Directory of Open Access Journals (Sweden) Tadeusz Kaczorek 2013-06-01 Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays. 11. Nonlinear noninteger order circuits and systems an introduction CERN Document Server Arena, P; Fortuna, L; Porto, D 2001-01-01 In this book, the reader will find a theoretical introduction to noninteger order systems, as well as several applications showing their features and peculiarities. The main definitions and results of research on noninteger order systems and modelling of physical noninteger phenomena are reported together with problems of their approximation. Control applications, noninteger order CNNs and circuit realizations of noninteger order systems are also presented.The book is intended for students and researchers involved in the simulation and control of nonlinear noninteger order systems, with partic 12. Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System Directory of Open Access Journals (Sweden) Zhenhua Hu 2013-01-01 Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states. 13. Fractional delayed damped Mathieu equation Science.gov (United States) Mesbahi, Afshin; Haeri, Mohammad; Nazari, Morad; Butcher, Eric A. 2015-03-01 This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. The n = 0 and n = 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special cases of the results for the current system. 14. Propagation of a general-type beam through a truncated fractional Fourier transform optical system. Science.gov (United States) Zhao, Chengliang; Cai, Yangjian 2010-03-01 Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping. 15. Advances in robust fractional control CERN Document Server Padula, Fabrizio 2015-01-01 This monograph presents design methodologies for (robust) fractional control systems. It shows the reader how to take advantage of the superior flexibility of fractional control systems compared with integer-order systems in achieving more challenging control requirements. There is a high degree of current interest in fractional systems and fractional control arising from both academia and industry and readers from both milieux are catered to in the text. Different design approaches having in common a trade-off between robustness and performance of the control system are considered explicitly. The text generalizes methodologies, techniques and theoretical results that have been successfully applied in classical (integer) control to the fractional case. The first part of Advances in Robust Fractional Control is the more industrially-oriented. It focuses on the design of fractional controllers for integer processes. In particular, it considers fractional-order proportional-integral-derivative controllers, becau... 16. Fractional-order active fault-tolerant force-position controller design for the legged robots using saturated actuator with unknown bias and gain degradation Science.gov (United States) Farid, Yousef; Majd, Vahid Johari; Ehsani-Seresht, Abbas 2018-05-01 In this paper, a novel fault accommodation strategy is proposed for the legged robots subject to the actuator faults including actuation bias and effective gain degradation as well as the actuator saturation. First, the combined dynamics of two coupled subsystems consisting of the dynamics of the legs subsystem and the body subsystem are developed. Then, the interaction of the robot with the environment is formulated as the contact force optimization problem with equality and inequality constraints. The desired force is obtained by a dynamic model. A robust super twisting fault estimator is proposed to precisely estimate the defective torque amplitude of the faulty actuator in finite time. Defining a novel fractional sliding surface, a fractional nonsingular terminal sliding mode control law is developed. Moreover, by introducing a suitable auxiliary system and using its state vector in the designed controller, the proposed fault-tolerant control (FTC) scheme guarantees the finite-time stability of the closed-loop control system. The robustness and finite-time convergence of the proposed control law is established using the Lyapunov stability theory. Finally, numerical simulations are performed on a quadruped robot to demonstrate the stable walking of the robot with and without actuator faults, and actuator saturation constraints, and the results are compared to results with an integer order fault-tolerant controller. 17. Skin rejuvenation and wrinkle reduction using a fractional radiofrequency system. Science.gov (United States) Hruza, George; Taub, Amy Forman; Collier, Susannah L; Mulholland, Stephen Robert 2009-03-01 Skin resurfacing has evolved rapidly over the past 15 years from ablative techniques to nonablative methods and most recently fractional ablative resurfacing. The purposes of this study were to analyze the degree of tissue ablation, coagulation, and heating; and to evaluate the clinical efficacy and safety of a fractional radiofrequency (RF) device, for the treatment of wrinkles with fractional skin ablation and coagulation. Individuals scheduled for abdominoplasty received fractional RF treatment to the abdomen area, using different tips at varying energy densities and coverage rates. Biopsies were performed ex vivo following abdominoplasty and tissue samples were routinely processed and stained, using hematoxylin and eosin). Another group of subjects received 3 facial treatments, scheduled at 3 to 4 week intervals. Clinical improvement and response to therapy were evaluated with standardized photography and clinical assessment by the subjects and investigators. Histological findings immediately posttreatment revealed demarcated zones of ablation/coagulation/necrosis and subnecrosis up to a depth of 450 microm. Higher energy levels generated deeper effects. We noticed a tunable balance between ablation and coagulation/necrosis. These effects were coverage mode and energy density dependent. Subjects undergoing facial treatment had minimal pain, no permanent side effects, or significant downtime. Investigators' assessment for improvement in skin texture correlated with subjects' evaluation and was greater than 40% for approximately 50% of subjects. Eighty percent of the subjects were satisfied with the results. Higher energy levels and lower coverage rates produced better aesthetic results along with less pain. The clinical observations and histological findings suggest that fractionated ablative skin resurfacing using a fractional radiofrequency device resulted in a safe, tolerable and effective improvement in skin texture and reduction of wrinkles. The depth of 18. Fractional Hunter-Saxton equation involving partial operators with bi-order in Riemann-Liouville and Liouville-Caputo sense Science.gov (United States) Gómez-Aguilar, J. F.; Atangana, Abdon 2017-02-01 In this work the fractional Hunter-Saxton equation applied in the study of diffusion of nematic liquid crystals was done involving partial operators with two fractional orders, α and β, via Atangana-Riemann and Atangana-Caputo with bi-order and via Riemann-Liouville, Caputo-Fabrizio-Riemann and Atangana-Baleanu-Riemann for the space domain. The mathematical equation underpinning this physical phenomenon was solved numerically using an iterative scheme where the numerical approximations for second order were developed. The new approach with two fractional orders is able to consider media with two different layers, scales and properties. The generalization of this equation exhibit different cases of anomalous behavior and the numerical solutions obtained describes the propagation of waves in a nematic liquid cristal. 19. Process and apparatus for fractionating close-boiling components of a multi-component system International Nuclear Information System (INIS) Tsao, U. 1983-01-01 A process and apparatus are described for the fractionation of close-boiling components of a multi-component system comprising at least two fractionation columns A, B in series having a plurality of equilibrium stages in which the vapor stream from a downstream fractionation column B is compressed by a compressor and passed into a lower portion of a preceding fractionation column A and a liquid bottom stream from any one of said columns except the last is expanded by an orifice sufficiently to convey the resulting liquid-vapor mixture to the upper portion of the next fractionation column B. In a particularly preferred embodiment, the compressed overhead vapor stream is passed in heat transfer relationship to a liquid stream withdrawn from the preceding fractionation column A prior to introduction into the lower portion of such preceding fractionation column A. In one of the claims, the multi-component close-boiling system is a deuterium oxide-water solution. (author) 20. On the Modelling and Control of a Laboratory Prototype of a Hydraulic Canal Based on a TITO Fractional-Order Model Directory of Open Access Journals (Sweden) Andres San-Millan 2017-08-01 Full Text Available In this paper a two-input, two-output (TITO fractional order mathematical model of a laboratory prototype of a hydraulic canal is proposed. This canal is made up of two pools that have a strong interaction between them. The inputs of the TITO model are the pump flow and the opening of an intermediate gate, and the two outputs are the water levels in the two pools. Based on the experiments developed in a laboratory prototype the parameters of the mathematical models have been identified. Then, considering the TITO model, a first control loop of the pump is closed to reproduce real-world conditions in which the water level of the first pool is not dependent on the opening of the upstream gate, thus leading to an equivalent single input, single output (SISO system. The comparison of the resulting system with the classical first order systems typically utilized to model hydraulic canals shows that the proposed model has significantly lower error: about 50%, and, therefore, higher accuracy in capturing the canal dynamics. This model has also been utilized to optimize the design of the controller of the pump of the canal, thus achieving a faster response to step commands and thus minimizing the interaction between the two pools of the experimental platform. 1. Asymptotic Solutions of Time-Space Fractional Coupled Systems by Residual Power Series Method Directory of Open Access Journals (Sweden) Wenjin Li 2017-01-01 Full Text Available This paper focuses on the asymptotic solutions to time-space fractional coupled systems, where the fractional derivative and integral are described in the sense of Caputo derivative and Riemann-Liouville integral. We introduce the Residual Power Series (for short RPS method to construct the desired asymptotic solutions. Furthermore, we apply this method to some time-space fractional coupled systems. The simplicity and efficiency of RPS method are shown by the application. 2. Ordering due to disorder in frustrated quantum magnetic system International Nuclear Information System (INIS) Yildirim, T. 1999-01-01 The phenomenon of order by disorder in frustrated magnetic systems is reviewed. Disorder (thermal or quantum fluctuations) may sometimes give rise to long range ordering in systems with frustration, where one must often consider the selection among classically degenerate ground states which are not equivalent by any symmetry. The lowest order effects of quantum fluctuations in such frustrated systems usually resolves the continues degeneracy of the ground state manifold into discrete Ising-type degeneracy. A unique ground state selection out of this Ising degenerate manifold then occurs due to higher order effects of quantum fluctuations. For systems such as face-centered cubic and body-centered tetragonal antiferromagnets where the number of Ising parameters to describe the ground state manifold is not macroscopic, we show that quantum fluctuations choose a unique ground state at the first order in 1/S 3. The order and volume fill rates in inventory control systems DEFF Research Database (Denmark) Thorstenson, Anders; Larsen, Christian 2011-01-01 This paper differentiates between an order (line) fill rate and a volume fill rate and specifies their performance for different inventory control systems. When the focus is on filling complete customer orders rather than total quantities the order fill rate would be the preferred service level...... measure. The main result shows how the order and volume fill rates are related in magnitude. Earlier results derived for a single-item, single-stage, continuous review inventory system with backordering and constant lead times controlled by a base-stock policy are extended in different directions... 4. Fractional Dynamics and Control CERN Document Server Machado, José; Luo, Albert 2012-01-01 Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics Develops new methods for control and synchronization of... 5. Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas. Science.gov (United States) Chevallier, Maguelonne; Krauth, Werner 2007-11-01 We discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose-Einstein condensation. Starting from the Landsberg recursion relation for the canonic partition function, we use elementary considerations to show that in a box of size L3 the sum of the cycle probabilities of length k>L2 equals the off-diagonal long-range order parameter in the thermodynamic limit. For arbitrary systems of ideal bosons, the integer derivative of the cycle probabilities is related to the probability of condensing k bosons. We use this relation to derive the precise form of the pik in the thermodynamic limit. We also determine the function pik for arbitrary systems. Furthermore, we use the cycle probabilities to compute the probability distribution of the maximum-length cycles both at T=0, where the ideal Bose gas reduces to the study of random permutations, and at finite temperature. We close with comments on the cycle probabilities in interacting Bose gases. 6. Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters International Nuclear Information System (INIS) Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A.; Delgado-Aguilera, Efredy 2016-01-01 This paper analyzes the synchronization of two fractional Lorenz systems in two cases: the first one considering fractional Lorenz systems with unknown parameters, and the second one considering known upper bounds on some of the fractional Lorenz systems parameters. The proposed control strategies use a reduced number of control signals and control parameters, employing mild assumptions. The stability of the synchronization errors is analytically demonstrated in all cases, and the convergence to zero of the synchronization errors is analytically proved in the case when the upper bounds on some system parameters are assumed to be known. Simulation studies are presented, which allows verifying the effectiveness of the proposed control strategies. 7. General solution for first order elliptic systems in the plane International Nuclear Information System (INIS) Mshimba, A.S. 1990-01-01 It is shown that a system of 2n real-valued partial differential equations of first order, which under certain assumptions can be transformed to the so-called 'complex normal form', admits a general solution. 15 refs 8. Fractional-Order Generalized Predictive Control: Application for Low-Speed Control of Gasoline-Propelled Cars Directory of Open Access Journals (Sweden) M. Romero 2013-01-01 Full Text Available There is an increasing interest in using fractional calculus applied to control theory generalizing classical control strategies as the PID controller and developing new ones with the intention of taking advantage of characteristics supplied by this mathematical tool for the controller definition. In this work, the fractional generalization of the successful and spread control strategy known as model predictive control is applied to drive autonomously a gasoline-propelled vehicle at low speeds. The vehicle is a Citroën C3 Pluriel that was modified to act over the throttle and brake pedals. Its highly nonlinear dynamics are an excellent test bed for applying beneficial characteristics of fractional predictive formulation to compensate unmodeled dynamics and external disturbances. 9. Simple numerical evaluation of modified Bessel functions Ksub(ν)(x) of fractional order and the integral ∫sup(infinitely)sub(x)Ksub(ν)(eta)d eta International Nuclear Information System (INIS) Kostroun, V.O. 1980-01-01 Theoretical expressions for the angular and spectral distributions of synchrotron radiation involve modified Bessel functions of fractional order and the integral ∫sup(infinitely)sub(x)Ksub(ν)(eta)d eta. A simple series expression for these quantities which can be evaluated numerically with hand-held programmable calculators is presented. (orig.) 10. A reduced order model of a quadruped walking system International Nuclear Information System (INIS) Sano, Akihito; Furusho, Junji; Naganuma, Nobuyuki 1990-01-01 Trot walking has recently been studied by several groups because of its stability and realizability. In the trot, diagonally opposed legs form pairs. While one pair of legs provides support, the other pair of legs swings forward in preparation for the next step. In this paper, we propose a reduced order model for the trot walking. The reduced order model is derived by using two dominant modes of the closed loop system in which the local feedback at each joint is implemented. It is shown by numerical examples that the obtained reduced order model can well approximate the original higher order model. (author) 11. Efficient Resource Allocation and Sectorization for Fractional Frequency Reuse (FFR in LTE Femtocell Systems Directory of Open Access Journals (Sweden) M. T. Kawser 2015-12-01 Full Text Available The Fractional Frequency Reuse (FFR is a resource allocation technique that can effectively mitigate inter-cell interference (ICI in LTE based HetNets and it is a promising solution. Various FFR schemes have been suggested to address the challenge of interference in femtocell systems. In this paper, we study the scopes of interference mitigation and capacity improvement. We propose a resource allocation scheme that gradually varies frequency resource share with distance from the eNodeB for both macrocells and femtocells in order to attain better utilization of the resources. This is performed effectively using three layers in the cell. The proposal also employs high number sectors in a cell, low interference and good frequency reuse. Monte-Carlo simulations are performed, which show that the proposed scheme achieves significantly better throughput compared to the existing FFR schemes. 12. Nonsingular Terminal Sliding Mode Control of Uncertain Second-Order Nonlinear Systems Directory of Open Access Journals (Sweden) Minh-Duc Tran 2015-01-01 Full Text Available This paper presents a high-performance nonsingular terminal sliding mode control method for uncertain second-order nonlinear systems. First, a nonsingular terminal sliding mode surface is introduced to eliminate the singularity problem that exists in conventional terminal sliding mode control. By using this method, the system not only can guarantee that the tracking errors reach the reference value in a finite time with high-precision tracking performance but also can overcome the complex-value and the restrictions of the exponent (the exponent should be fractional number with an odd numerator and an odd denominator in traditional terminal sliding mode. Then, in order to eliminate the chattering phenomenon, a super-twisting higher-order nonsingular terminal sliding mode control method is proposed. The stability of the closed-loop system is established using the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the proposed method. 13. The order and volume fill rates in inventory control systems DEFF Research Database (Denmark) Thorstenson, Anders; Larsen, Christian 2014-01-01 This paper differentiates between an order (line) fill rate and a volume fill rate and specifies their performance for different inventory control systems. When the focus is on filling complete customer orders rather than total demanded quantity the order fill rate would be the preferred service...... level measure. The main result shows how the order and volume fill rates are related in magnitude. Earlier results derived for a single-item, single-stage, continuous review inventory system with backordering and constant lead times controlled by a base-stock policy are extended in different directions...... extensions consider more general inventory control review policies with backordering, as well as some relations between service measures. A particularly important result in the paper concerns an alternative service measure, the customer order fill rate, and shows how this measure always exceeds the other two... 14. A NEW FRACTIONAL MODEL OF SINGLE DEGREE OF FREEDOM SYSTEM, BY USING GENERALIZED DIFFERENTIAL TRANSFORM METHOD Directory of Open Access Journals (Sweden) HASHEM SABERI NAJAFI 2016-07-01 Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point. 15. State-Space Modelling of Loudspeakers using Fractional Derivatives DEFF Research Database (Denmark) King, Alexander Weider; Agerkvist, Finn T. 2015-01-01 This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data... 16. The search for competing charge orders in frustrated ladder systems International Nuclear Information System (INIS) Lal, Siddhartha; Laad, Mukul S. 2007-08-01 A recent study revealed the dynamics of the charge sector of a one-dimensional quarter- filled electronic system with extended Hubbard interactions to be that of an effective pseudospin transverse-field Ising model (TFIM) in the strong coupling limit. With the twin motivations of studying the co-existing charge and spin order found in strongly correlated chain systems and the effects of inter-chain couplings, we investigate the phase diagram of coupled effective (TFIM) systems. A bosonisation and RG analysis for a two-leg TFIM ladder yields a rich phase diagram showing Wigner/Peierls charge order and Neel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Kosterlitz-Thouless transitions are found to lead from the gapless phase to either of the charge-ordered phases. Low energy effective Hamiltonian analyses of a strongly coupled 2-chain ladder system confirm a phase diagram with in-chain CO, rung-dimer, and orbital antiferromagnetic ordered phases with varying interchain couplings as well as superconductivity upon hole-doping. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled chain and ladder systems. (autor) 17. Fractional thermoelasticity CERN Document Server Povstenko, Yuriy 2015-01-01 This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research. The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators. This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of ... 18. Finite time blow-up of solutions for a nonlinear system of fractional differential equations Directory of Open Access Journals (Sweden) Abdelaziz Mennouni 2017-06-01 Full Text Available In this article we study the blow-up in finite time of solutions for the Cauchy problem of fractional ordinary equations $$\\displaylines{ u_{t} +a_1\\,^{c}D_{0_{+}}^{\\alpha_1} u +a_2\\,^{c}D_{0_{+}}^{\\alpha_2} u+\\dots +a_{n}\\,^{c}D_{0_{+}}^{\\alpha_n} u =\\int_0^{t} \\frac{(t-s^{-\\gamma_1}}{ \\Gamma(1-\\gamma_1 }f(u(s,v(sds,\\cr v_{t} +b_1\\,^{c}D_{0_{+}}^{\\beta_1} v+ b_2\\,^{c}D_{0_{+}}^{\\beta_2} v+\\dots +b_{n}\\,^{c}D_{0_{+}}^{\\beta_n} v = \\int_0^{t} \\frac{(t-s^{-\\gamma_2}}{ \\Gamma(1-\\gamma_2 }g(u(s,v(sds, }$$ for t>0, where the derivatives are Caputo fractional derivatives of order$\\alpha_i, \\beta_i\$, and f and g are two continuously differentiable functions with polynomial growth. First, we prove the existence and uniqueness of local solutions for the above system supplemented with initial conditions, then we establish that they blow-up in finite time.

19. Mixed H ∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

Science.gov (United States)

Song, Xiao-Na; Song, Shuai; Tejado Balsera, Inés; Liu, Lei-Po

2017-10-01

This paper investigates the mixed H ∞ and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H ∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H ∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method. Supported by National Natural Science Foundation of China under Grant Nos. U1604146, U1404610, 61473115, 61203047, Science and Technology Research Project in Henan Province under Grant Nos. 152102210273, 162102410024, and Foundation for the University Technological Innovative Talents of Henan Province under Grant No. 18HASTIT019

20. Computerized Physician Order Entry - effectiveness and efficiency of electronic medication ordering with decision support systems.

Science.gov (United States)

Stürzlinger, Heidi; Hiebinger, Cora; Pertl, Daniela; Traurig, Peter

2009-05-19

Computerized physician order entry (CPOE) systems are software to electronically enter medication orders. They can be equipped with tools for decision support (CDS). In Germany, various vendors offer such systems for hospitals and physicians' offices. These systems have mostly been developed during the last five to ten years. CPOE-systems exist since the 1970's. Usually, clinical decision support is integrated into the CPOE to avoid errors. This HTA-report aims to evaluate the effectiveness and efficiency of CPOE-/CDS-systems and their ethical, social and legal aspects. The systematic literature search (27 international data bases) yielded 791 abstracts. Following a two-part selection process, twelve publications were included in the assessment. All reviews and studies included in the present report show that the use of CPOE-/CDS-systems can lead to a reduction of medication errors. Minor errors can be eliminated almost completely. The effect of CPOE-/CDS-systems on the rate of adverse drug events (ADE) is evaluated in only two primary studies with conflicting results. It is difficult to compare the results of economical studies because they evaluate different settings, interventions and time frames. In addition, the documentation often is not fully transparent. All four studies included measure costs and effects from the perspective of a hospital or hospital affiliation. Concerning social aspects, the literature points at changes regard competing interests of technology and humans that result from the implementation of CPOE-systems. The experience of institutions in which the implementation of CPOE-systems leads to problems showed that the importance of considering the socio-organisational context had partly been underestimated. CPOE-/CDS-systems are able to reduce the rate of medication errors when ordering medications. The adherence to guidelines, communication, patient care and personnel satisfaction can also be affected positively. However, the literature also

1. Computerized Physician Order Entry - effectiveness and efficiency of electronic medication ordering with decision support systems

Directory of Open Access Journals (Sweden)

Traurig, Peter

2009-05-01

Full Text Available Health political background: Computerized physician order entry (CPOE systems are software to electronically enter medication orders. They can be equipped with tools for decision support (CDS. In Germany, various vendors offer such systems for hospitals and physicians’ offices. These systems have mostly been developed during the last five to ten years. Scientific background: CPOE-systems exist since the 1970’s. Usually, clinical decision support is integrated into the CPOE to avoid errors. Research questions: This HTA-report aims to evaluate the effectiveness and efficiency of CPOE-/CDS-systems and their ethical, social and legal aspects. Methods: The systematic literature search (27 international data bases yielded 791 abstracts. Following a two-part selection process, twelve publications were included in the assessment. Results: All reviews and studies included in the present report show that the use of CPOE-/CDS-systems can lead to a reduction of medication errors. Minor errors can be eliminated almost completely. The effect of CPOE-/CDS-systems on the rate of adverse drug events (ADE is evaluated in only two primary studies with conflicting results. It is difficult to compare the results of economical studies because they evaluate different settings, interventions and time frames. In addition, the documentation often is not fully transparent. All four studies included measure costs and effects from the perspective of a hospital or hospital affiliation. Concerning social aspects, the literature points at changes regard competing interests of technology and humans that result from the implementation of CPOE-systems. The experience of institutions in which the implementation of CPOE-systems leads to problems showed that the importance of considering the socio-organisational context had partly been underestimated. Discussion: CPOE-/CDS-systems are able to reduce the rate of medication errors when ordering medications. The adherence to

2. Improved system blind identification based on second-order ...

An improved system blind identification method based on second-order cyclostationary statistics and the properties of group delay, has been proposed. This is achieved by applying a correction to the estimated phase (by the spectral correlation density of the system output) for the poles, in the group delay domain.

3. Order picking in carousel systems under the nearest item heuristic

NARCIS (Netherlands)

Litvak, Nelli; Adan, I.J.B.F.; Wessels, J.; Zijm, Willem H.M.

2000-01-01

A carousel is a computer controlled warehousing system, which is widely used to store small and medium sized goods. One of the most important performance characteristics of such systems is the pick time of an order, which mostly depends on the travel time of the carousel. In this paper we consider

4. Improved system blind identification based on second-order ...

However, many systems, like data commu- nication channels, acoustic paths and vocal tract, are of non-minimum phase nature and their actual identification is essential. Higher order statistics (HOS), like the bispectrum, have complete system phase information in a hidden manner and many methods to extract phase from ...

5. Contribution to the modelling of induction machines by fractional order; Contribution a la modelisation dynamique d'ordre non entier de la machine asynchrone a cage

Energy Technology Data Exchange (ETDEWEB)

Canat, S.

2005-07-15

Induction machine is most widespread in industry. Its traditional modeling does not take into account the eddy current in the rotor bars which however induce strong variations as well of the resistance as of the resistance of the rotor. This diffusive phenomenon, called 'skin effect' could be modeled by a compact transfer function using fractional derivative (non integer order). This report theoretically analyzes the electromagnetic phenomenon on a single rotor bar before approaching the rotor as a whole. This analysis is confirmed by the results of finite elements calculations of the magnetic field, exploited to identify a fractional order model of the induction machine (identification method of Levenberg-Marquardt). Then, the model is confronted with an identification of experimental results. Finally, an automatic method is carried out to approximate the dynamic model by integer order transfer function on a frequency band. (author)

6. Nonsymmetric Interactions Trigger Collective Swings in Globally Ordered Systems

Science.gov (United States)

Cavagna, Andrea; Giardina, Irene; Jelic, Asja; Melillo, Stefania; Parisi, Leonardo; Silvestri, Edmondo; Viale, Massimiliano

2017-03-01

Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In condensed matter systems, order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing with system size. Several biological systems, however, are less stable and spontaneously change their global state on relatively short time scales. Here we show that there are two crucial ingredients in these systems that enhance the effect of noise, leading to collective changes of state on finite time scales and off-equilibrium behavior: the nonsymmetric nature of interactions between individuals, and the presence of local heterogeneities in the topology of the network. Our results might explain what is observed in several living systems and are consistent with recent experimental data on bird flocks and other animal groups.

7. Interactions of mercury with different molecular weight fractions of humic substances in aquatic systems.

Digital Repository Service at National Institute of Oceanography (India)

Chakraborty, P.; Yao, K.M.; Chennuri, K.; Vudamala, K.; Babu, P.V.R.

Interactions of mercury (Hg) with different molecular weight fractions of humic substances (HS) play an important role in controlling distribution, diffusion, speciation, and bioavailability of Hg in natural systems. This study suggests that Hg...

8. Infinite-order symmetries for quantum separable systems

International Nuclear Information System (INIS)

Miller, W.; Kalnins, E.G.; Kress, J.M.; Pogosyan, G.S.

2005-01-01

A calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space is developed. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, it can develop a calculus for conformal symmetries of the time-dependent Schroedinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries [ru

9. Infinite-Order Symmetries for Quantum Separable Systems

International Nuclear Information System (INIS)

Miller, W.; Kalnins, E.G.; Kress, J.M.; Pogosyan, G.S.

2005-01-01

We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, we can develop a calculus for conformal symmetries of the time-dependent Schroedinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries

10. Perturbation of Fractional Multi-Agent Systems in Cloud Entropy Computing

Directory of Open Access Journals (Sweden)

Rabha W. Ibrahim

2016-01-01

Full Text Available A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural approaches, and algorithms. In this study, we introduce a new perturbed algorithm based on the fractional Poisson process. The discrete dynamics are suggested by using fractional entropy and fractional type Tsallis entropy. Moreover, we study the algorithm stability.

11. FRACTIONAL BANKING

OpenAIRE

Maria Klimikova

2010-01-01

Understanding the reasons of the present financial problems lies In understanding the substance of fractional reserve banking. The substance of fractional banking is in lending more money than the bankers have. Banking of partial reserves is an alternative form which links deposit banking and credit banking. Fractional banking is causing many unfavorable economic impacts in the worldwide system, specifically an inflation.

12. The second hyperpolarizability of systems described by the space-fractional Schrödinger equation

Science.gov (United States)

Dawson, Nathan J.; Nottage, Onassis; Kounta, Moussa

2018-01-01

The static second hyperpolarizability is derived from the space-fractional Schrödinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second hyperpolarizability for a space-fractional quantum system. The total oscillator strength is shown to decrease as the space-fractional parameter α decreases, which reduces the optical response of a quantum system in the presence of an external field. This damped response is caused by the wavefunction dependent position and momentum commutation relation. Although the maximum response is damped, we show that the one-dimensional quantum harmonic oscillator is no longer a linear system for α ≠ 1, where the second hyperpolarizability becomes negative before ultimately damping to zero at the lower fractional limit of α → 1 / 2.

13. Dynamic scaling of topological ordering in classical systems

Science.gov (United States)

Xu, Na; Castelnovo, Claudio; Melko, Roger G.; Chamon, Claudio; Sandvik, Anders W.

2018-01-01

We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional Z2 (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a nonlocal order parameter (defined using Wilson loops) and a dynamic exponent z =2.70 ±0.03 , the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature—the Ising chain, the two-dimensional Z2 gauge model, and a three-dimensional star model (another variant of the Z2 gauge model). In these systems the correlation length diverges exponentially, in a way that is nonsmooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface.

14. Stabilization of third-order bilinear systems using constant controls

Directory of Open Access Journals (Sweden)

A. E. Golubev

2014-01-01

Full Text Available This paper deals with the zero equilibrium stabilization for dynamical systems that have control input singularities. A dynamical system with scalar control input is called nonregular if the coefficient of input becomes null on a subset of the phase space that contains the origin. One of the classes of nonregular dynamical systems is represented by bilinear systems. In case of second-order bilinear systems the necessary and sufficient conditions for the zero equilibrium stabilizability are known in the literature. However, in general case the stabilization problem in the presence of control input singularities has not been solved yet.In this note we solve the problem of the zero equilibrium stabilization for the third-order bilinear dynamical systems given in a canonical form. The solution is found in the class of constant controls. The necessary and sufficient conditions are obtained for the zero equilibrium stabilizability of the bilinear systems in question.The dependence of the zero equilibrium stabilizability on system parameter values is analyzed. The general criteria of stabilizability by means of constant controls are given for the bilinear systems in question. In case when all the system parameters have nonzero values the necessary and sufficient stabilizability conditions are proved. The case when some of the parameters are equal to zero is also considered.Further research can be focused on extending the obtained results to a higher-order case of bilinear and affine dynamical systems. The solution of the considered stabilization problem should also be found not only within constant controls but also in a class of state feedbacks, particularly, in the case when stabilizing constant control does not exist.One of the potential application areas for the obtained theoretical results is automatic control of technical plants like unmanned aerial vehicles and mobile robots.

15. Ordering kinetics in model systems with inhibited interfacial adsorption

DEFF Research Database (Denmark)

Willart, J.-F.; Mouritsen, Ole G.; Naudts, J.

1992-01-01

. The results are related to experimental work on ordering processes in orientational glasses. It is suggested that the experimental observation of very slow ordering kinetics in, e.g., glassy crystals of cyanoadamantane may be a consequence of low-temperature activated processes which ultimately lead......The ordering kinetics in two-dimensional Ising-like spin moels with inhibited interfacial adsorption are studied by computer-simulation calculations. The inhibited interfacial adsorption is modeled by a particular interfacial adsorption condition on the structure of the domain wall between......, of the algebraic growth law, R(t)∼Atn, whereas the growth exponent, n, remains close to the value n=1/2 predicted by the classical Lifshitz-Allen-Cahn growth law for systems with nonconserved order parameter. At very low temperatures there is, however, an effective crossover to a much slower algebraic growth...

16. Parts-of-speech systems and word order

DEFF Research Database (Denmark)

Hengeveld, Kees; Rijkhoff, Jan; Siewierska, Anna

2004-01-01

the functions of two or more of the traditional word classes, other strategies have to be invoked to enhance identifiability. In these languages word order constraints are used to make syntactic slots identifiable on the basis of their position within the clause or phrase. Hence the word order possibilities......This paper argues that the word order possibilities of a language are partly determined by the parts-of-speech system of that language. In languages in which lexical items are specialized for certain functionally defined syntactic slots (e.g. the modifier slot within a noun phrase......), the identifiability of these slots is ensured by the nature of the lexical items (e.g. adjectives) themselves. As a result, word order possibilities are relatively unrestricted in these languages. In languages in which lexical items are not specialized for certain syntactic slots, in that these items combine...

17. Third-order superintegrable systems separating in polar coordinates

Energy Technology Data Exchange (ETDEWEB)

Tremblay, Frederick; Winternitz, Pavel, E-mail: tremblaf@crm.umontreal.c, E-mail: wintern@crm.umontreal.c [Centre de Recherches Mathematiques and Departement de Mathematiques et de Statistique, Universite de Montreal, C.P. 6128, succ. Centre-Ville, Montreal, QC H3C 3J7 (Canada)

2010-04-30

A complete classification of quantum and classical superintegrable systems in E{sub 2} is presented that allow the separation of variables in polar coordinates and admit an additional integral of motion of order 3 in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painleve transcendent or in terms of the Weierstrass elliptic function.

18. Expanding Evolutionary Theory beyond Darwinism with Elaborating, Self-Organizing, and Fractionating Complex Evolutionary Systems

Science.gov (United States)

Fichter, Lynn S.; Pyle, E. J.; Whitmeyer, S. J.

2010-01-01

Earth systems increase in complexity, diversity, and interconnectedness with time, driven by tectonic/solar energy that keeps the systems far from equilibrium. The evolution of Earth systems is facilitated by three evolutionary mechanisms: "elaboration," "fractionation," and "self-organization," that share…

19. Ordering fluctuations in a shear-banding wormlike micellar system

DEFF Research Database (Denmark)

Angelico, R.; Rossi, C. Oliviero; Ambrosone, L.

2010-01-01

We present a first investigation about the non-linear flow properties and transient orientational-order fluctuations observed in the shear-thinning lecithin–water–cyclohexane wormlike micellar system at a concentration near to the zero-shear isotropic–nematic phase transition. From rheological...

20. PID control of second-order systems with hysteresis

NARCIS (Netherlands)

Jayawardhana, Bayu; Logemann, Hartmut; Ryan, Eugene P.

2008-01-01

The efficacy of proportional, integral and derivative (PID) control for set point regulation and disturbance rejection is investigated in a context of second-order systems with hysteretic components. Two basic structures are studied: in the first, the hysteretic component resides (internally) in the