Journal ArticleDOI
Stability analysis of linear fractional differential system with multiple time delays
Reads0
Chats0
TLDR
In this paper, the stability of an n-dimensional linear fractional differential equation with time delays was studied, where the delay matrix is defined in (R+n×n).Abstract:
In this paper, we study the stability of n-dimensional linear fractional differential equation with time delays, where the delay matrix is defined in (R+)n×n. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. As its an application, we apply our theorem to the delayed system in one spatial dimension studied by Chen and Moore [Nonlinear Dynamics29, 2002, 191] and determine the asymptotically stable region of the system. We also deal with synchronization between the coupled Duffing oscillators with time delays by the linear feedback control method and the aid of our theorem, where the domain of the control-synchronization parameters is determined.read more
Citations
More filters
Book
Fractional Order Systems: Modeling and Control Applications
TL;DR: Fractional Order Systems Fractional order PID Controller Chaotic fractional order systems Field Programmable Gate Array, Microcontroller and Field Pmable Analog Array Implementation Switched Capacitor and Integrated Circuit Design Modeling of Ionic Polymeric Metal Composite as discussed by the authors.
Journal ArticleDOI
LMI stability conditions for fractional order systems
TL;DR: Under commensurate order hypothesis, it is shown that a direct extension of the second Lyapunov's method is a tedious task, and through a direct stability domain characterization, three LMI stability analysis conditions are proposed.
Journal ArticleDOI
A survey on the stability of fractional differential equations - Dedicated to Prof. Y.S. Chen on the Occasion of his 80th Birthday
TL;DR: A brief overview on the recent stability results of fractional differential equations and the analytical methods used are provided in this paper, where some conclusions for stability are similar to that of classical integer-order differential equations.
Journal ArticleDOI
Chaotic attractors in incommensurate fractional order systems
TL;DR: In this paper, a necessary condition is given to check the existence of 1-scroll, 2-scroll or multi-scroll chaotic attractors in a fractional order system, based on the stability theorems in fractional differential equations.
Journal ArticleDOI
Numerical methods for solving the multi-term time-fractional wave-diffusion equation
TL;DR: Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations and can be extended to other kinds of themulti-term fractional time-space models with fractional Laplacian.
References
More filters
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Introduction to Functional Differential Equations
TL;DR: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977 and attempts to maintain the spirit of that book and have retained approximately one-third of the material intact.
Book
A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations
TL;DR: In this paper, an Adams-type predictor-corrector method for the numerical solution of fractional differential equations is discussed, which may be used both for linear and nonlinear problems, and it may be extended tomulti-term equations (involving more than one differential operator) too.
Proceedings Article
Stability results for fractional differential equations with applications to control processing
TL;DR: In this article, stability results for finite-dimensional linear fractional differential systems in state-space form are given for both internal and external stability, and the main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector.