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An Efficient Non-standard Finite Difference Scheme for a Class of Fractional Chaotic Systems

[+] Author and Article Information
Mojtaba Hajipour

Department of Mathematics, Sahand University of Technology, Tabriz, Iran
hajipour@sut.ac.ir

Amin Jajarmi

Department of Electrical Engineering, University of Bojnord, P.O. Box: 94531-1339, Bojnord, Iran
a.jajarmi@ub.ac.ir

Dumitru Baleanu

Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey; Institute of Space Sciences, P.O.Box, MG-23, R 76900, Magurele-Bucharest, Romania
dumitru@cankaya.edu.tr

1Corresponding author.

ASME doi:10.1115/1.4038444 History: Received November 02, 2016; Revised November 01, 2017

Abstract

In this paper we formulate a new non-standard finite difference scheme to study the dynamic treatments of a class of fractional chaotic systems. To design the new proposed scheme, an appropriate non-local framework is applied for the discretization of the nonlinear terms. This method is easy to implement and preserves some important physical properties of the considered model, e.g. fixed points and their stability. Additionally, this scheme is explicit and inexpensive to solve fractional differential equations. From a practical point of view, the stability analysis and chaotic behavior of three novel fractional systems are provided by the proposed approach. Numerical simulations and comparison results confirm that this scheme is also successful for the fractional chaotic systems with delay arguments.

Copyright (c) 2017 by ASME; use license CC-BY 4.0
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