Novel chaotic systems with fractional differential operators: Numerical approaches

N.H. Sweilam, S.M. AL - Mekhlafi and D.G. Mohamed

Chaos, Solitons & Fractals, 2021, vol. 142, issue C

Abstract: The purpose of this paper is to study numerically the behavior of two novel different classes of fractional order chaotic systems. These systems are; the fractal-fractional hyperchaotic finance system and the fractal-fractional Bloch system with time delay. The fractal-fractional derivatives are defined in the Caputo and Riemann-Liouville senses. Two Grünwald-Letnikov nonstandard finite difference schemes are presented to study the proposed chaotic systems. Moreover the stability analysis of the used methods are proved. In order to show the simplicity and effectively of the proposed methods, numerical simulations and comparative studies are given.

Keywords: Fractal-fractional chaotic systems; Grünwald-Letnikov nonstandard finite difference method; Hyperchaotic finance system; Bloch system, (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308675

DOI: 10.1016/j.chaos.2020.110475

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