AUTHOR=Ghanbari Behzad , Nisar Kottakkaran Sooppy 

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00192

DOI=10.3389/fphy.2020.00192

ISSN=2296-424X

ABSTRACT=Chaotic systems are dynamical systems that are highly sensitive to initial conditions. Such models appear in the modeling of many real-world phenomena in science and engineering. The main purpose of this paper is to present several efficient numerical treatments in chaotic systems including fractal-fractional operators. Several numerical examples test the performance of the methods presented. The simulation result for different values of fractional and fractal parameters are also included in the paper. It is readily proved that the fractal-fractional derivative will enable us to capture all the valuable information from the history of the phenomena under consideration. The numerical scheme can also be implemented for other chaotic systems with fractal fractional operators.