ABSTRACT
A range of chaotic and hyperchaotic processes were modelled with the Atangana-Baleanu fractional derivative that has both non-local and non-singular properties in the sense of Caputo. A modified Chua chaotic attractor has been extended and analyzed within the scope of fractional differentiation and integration. Three cases of fractional differential operators are considered, namely the Caputo, Caputo-Fabrizio and the Atangana-Baleanu derivatives. We apply the fixed point theory and approximation method to show the existence and uniqueness of solutions due to non-linearity of this modified model, and we used a user-friendly scheme to provide numerical solutions.
