Mathematical Analysis and Numerical Simulation of Chaotic Noninteger Order Differential Systems with Riemann-Liouville Derivative

Abstract

This article deals with the design, analysis, and implementation of a robust numerical scheme when applied to time-fractional reaction-diffusion system. Stability analysis and numerical treatment of chaotic fractional differential system in Riemann-Liouville sense are considered in this article. Simulation results show that chaotic phenomena can only occur if the reaction or local dynamics of such system is coupled or nonlinear in nature. Illustrative examples that are still of current and recurring interest to economists, engineers, mathematicians and physicists are chosen, to describe the points and queries that may arise. Numerical results presented agree with the theoretical findings.