In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate fractional order Liu systems are investigate...

The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classical theory of linear viscoelasticity, we contrast these two types of fractional derivatives in thei...

In this paper, by utilizing the fractional calculus theory and computer simulations, dynamics of the fractional order system is studied. Further, we have extended the nonlinear feedback control in ODE systems to fractional order systems, in order to eliminate the chaotic behavior. The results are proved analytically by stability condition for fractional order system. Moreover numerical simulati...

In this paper, the authors considered a class of fractional-order Hindmarsh-Rose (HR) neuron model with time-delays and widely investigated the dynamical behaviors of considered fractional-order HR model with time-delays. Some new sufficient conditions are derived by using the proposed stability theory of linear fractional-order systems to guarantee the stability results of fractional-order HR ...

This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS) for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems...

The theory of differential and integral equations of fractional order has recently received a lot of attention and now constitutes a significant branch of nonlinear analysis. Numerous research papers and monographs have appeared devoted to differential and integral equations of fractional order cf., e.g., 1–6 . These papers contain various types of existence results for equations of fractional ...

The dynamic behavior of fractional order systems have received increasing attention in recent years, In this paper the reliable phase synchronization problem between two coupled chaotic fractional order system with varying time is constructed, An active delay expected synchronization between two coupled chaotic fractional order systems and hyperchaotic fractional order systems is analyzed by ut...

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...