Abstract: Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we de...

We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant FO-LTI systems. To determine the control parameters, one needs only a little knowledg...

Based on linear feedback control technique, a projective synchronization scheme ofN-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stab...

The theory of derivative of noninteger order goes back to Leibniz, Liouville, Riemann, Grunwald and Letnikov. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics, medicine.Classes of fractional differentiable systems have studied in [10], [4]. In the first section the fractional tangent bundle to a differentiable manifold is defined, u...

Fractional calculus (differentiation and integration of arbitrary order) arise naturally in various areas of applied science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and image processing, polymer rheology, regular variation in thermodynamics, biophysics, blood flow phenomena, aerodynamics, electro-dynamics of complex medium, viscoelas...

An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. Alaboratory experimental system shows preliminary results that demonstrate the proposed theory. Applications such as anamorphic fractional correlation and multiplexing in fractional domains...

Since the complexity of the practical environment, many distributed networked systems can not be illustrated with the integer-order dynamics and only be described as the fractional-order dynamics. Suppose multi-agent systems will show the individual diversity with difference agents, where the heterogeneous (integerorder and fractional-order) dynamics are used to illustrate the agent systems and...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

We provide the main features of Lyapunov theory when it is formulated for fractional order systems. We give consistent extensions of Lyapunov, LaSalle and Chetaev classical theorems to the case of fractional order systems. We give examples to illustrate the applications of the concepts and propositions introduced. © 2016 Elsevier Inc. All rights reserved.

This paper deals with feedback control of fractional-order Chua’s system. The fractional-order Chua’s system with total order less than three which exhibit chaos as well as other nonlinear behavior and theory for control of chaotic systems using sampled data are presented. Numerical experimental example is shown to verify the theoretical results.