Novel chaotic systems with fractional differential operators: Numerical approaches

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 Grunwald-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. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper numerically studies the behavior of two novel classes of fractional order chaotic systems, with fractal-fractional derivatives defined in the Caputo and Riemann-Liouville senses. Two Grunwald-Letnikov nonstandard finite difference schemes are presented for studying these systems, and the stability analysis of the methods is proved. Numerical simulations and comparative studies are used to demonstrate the simplicity and effectiveness of the proposed methods.