Some Effective Numerical Techniques for Chaotic Systems Involving Fractal-Fractional Derivatives With Different Laws

Abstract

Chaotic systems are dynamical systems that are highly sensitive to initial conditions. Such systems are used to model many real-world phenomena in science and engineering. The main purpose of this paper is to present several efficient numerical treatments for chaotic systems involving fractal-fractional operators. Several numerical examples test the performance of the proposed methods. Simulations with different values of the fractional and fractal parameters are also conducted. It is demonstrated that the fractal-fractional derivative enables one to capture all the useful information from the history of the phenomena under consideration. The numerical schemes can also be implemented for other chaotic systems with fractal-fractional operators.