Discrete chaos in fractional sine and standard maps

Self Cite

Section: Introductionmentioning

confidence: 99%

Maximum principles for time-fractional Caputo-Katugampola diffusion equations

Cao¹,

Kong²,

Zeng³

2017

Self Cite

“…In the last thirty years or so, the theory of (FC) has produced an abundance of important results both in pure and applied mathematics as well as in other fields as for example: physics, chemistry, biology, economics, control theory, signal and image processing, biophysics, blood flow phenomena, aerodynamics, fitting of experimental data, etc. (see [11-13, 22, 28-31]), as it is allowed mathematical formulations for new classes of interesting problems (see [3,5,6,19,20,23,32]). …”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions

Bai¹,

Kong²

2017

The purpose of this paper is devoted to consider the existence of solutions for a class of nonlinear Caputo-Hadamard fractional differential equations with integral terms ((CHFDE), for short). Firstly, by applying the semi-group property of Hadamard fractional integral operator, a necessary condition of solvability for (CHFDE) is established. Then, under the suitable conditions, we prove the solution set of (CHFDE) is nonempty by using the method of upper and lower solutions, and Arzelà-Ascoli theorem. Finally, we present several numerical examples to explicate the main results.

“…Issues in topics such as, the synchronization of order chaotic systems in a broad variety of situations and the use of fractional order chaotic dynamics for various purposes, are at the forefront of recent application topics in nonlinear science. These topics unites the knowledge of basic mathematical properties of fractional order chaos and specific practical considerations of various applications [7,15,19,26,27,31,32]. Synchronization of chaotic system with integer order is understood well since the pioneering work by Pecora and Carrol [18].…”

Section: Introductionmentioning

confidence: 99%

Projective reduce order synchronization of fractional order chaotic systems with unknown parameters

Al-Sawalha¹

2017

This paper, mainly concerns the adaptive projective reduce order synchronization behavior of uncertain chaotic system. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of two chaotic and hyperchaotic systems asymptotically synchronized up to a desired identical and different scaling matrix. Numerical simulation results show that the proposed method is effective, convenient, and also faster for projective dual synchronization of chaotic and hyperchaotic systems.