Coexistence of multi-scroll chaotic attractors for a three-dimensional quadratic autonomous fractional system with non-local and non-singular kernel

In this paper, we present a numerical scheme and mathematical analysis for the famous three-dimensional quadratic autonomous self-govern system that happens to be chaotic with the coexistence of multi-scroll attractors. The scheme is based on the Atangana-Baleanu fractional derivative in the Caputo sense. The formulation of these schemes introduces the non-local and non-singular kernel to the fractional derivatives. The fractional derivative is then approximated using the family of the Adams-Bashforth schemes. The results are presented in both numerical and graphical as the fractional order beta varies between 0 < beta <= 1. We study the proposed model in the both generalized case that is 0 < beta < 1 and the case where beta = 1, which is the integer standard case. Due to the impact of the generalized case, the proposed model is able to maintain the coexistence of multi-scroll attractors. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).