The dynamics of a new chaotic system through the Caputo-Fabrizio and Atanagan-Baleanu fractional operators

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo-Fabrizio and the Atangana-Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo-Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana-Baleanu operator, and present their analysis. The Atangana-Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter alpha. We show that at the integer case, both the models (in Caputo-Fabrizio sense and the Atangana-Baleanu sense) give the same results.