The fractional order calculus theory and its modeling methods have been applied widely in control field. And design of fractional order control systems become hot point of recent years. This paper establishes fractional order systems which parameters are obtained by Bode’s ideal transfer function method to get the desired frequency response. Apply this method a new control structure of fraction...

In this paper, the class of continuous-time linear systems is enlarged with the inclusion of the fractionallinear systems. These are systems described by fractional differential equations. It is shown how to compute theimpulse, step, and frequency responses from the transfer function. The theory is supported by definitions offractional derivative and integral, generalisations of the...

Synchronization of chaotic and Lu system has been done using the active sliding mode control strategy. Regarding the synchronization task as a control problem, fractional order mathematics is used to express the system and active sliding mode for synchronization. It has been shown that, not only the performance of the proposed method is satisfying with an acceptable level of control signal, but...

By introducing the fractional derivatives in the sense of caputo, we use the Adomian decomposition method to construct the approximate solutions for some fractional partial differential equations with time and space fractional derivatives via the time and space fractional derivatives wave equation, the time and space fractional derivatives reduced wave equation and the (1+1)-dimensional Burger’...

1 School of Mathematical Sciences, Queensland University of Technology, P.O. Box 2434, Brisbane, QLD 4001, Australia 2 Department of Bioengineering, University of Illinois, 851 South Morgan Street, Chicago, IL 60607, USA 3Department of Mathematics, Shanghai University, Shanghai 200444, China 4Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA 5Depar...

The problem of the dual synchronization of two different fractional-order chaotic systems is studied. By a linear controller, we realize the dual synchronization of fractional-order chaotic systems. Finally, the proposed method is applied for dual synchronization of Van der Pol-Willis systems and Van der Pol-Duffing systems. The numerical simulation shows the accuracy of the theory.

This paper investigates the stability of n-dimensional nonlinear fractional differential systems with Riemann-Liouville derivative. By using the Mittag-Leffler function, Laplace transform and the Gronwall-Bellman lemma, one sufficient condition is attained for the asymptotical stability of a class of nonlinear fractional differential systems whose order lies in (0, 2). According to this theory,...

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme.

This paper is concerned with the controllability of linear fractional differential systems with delay in state and impulses.The factors of such systems including fractional derivative, impulses, and delay are taken into account synchronously. The expression of state response for such systems is derived, and the sufficient and necessary conditions of controllability criteria are established. Bot...