Anis Shabani - Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Amir Hossein Refahi Sheikhani - Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Hossein Aminikhah - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

In this article, we investigated the robust control approach for variable-order fractional time fractional butterfly- shaped chaotic attractor system that the fractional derivative is considered in Atangana-Baleanu-Caputo sense. We show the computational algorithm with high accuracy for solving the proposed systems. For the suggested system, Adams-Bashforth-Moulton approach applied for converting the system of the equations into a system of linear or nonlinear algebraic equations. The existence and uniqueness of the solution are shown and also asymptotically stable is investigated in this article. At the end, a number of statistical indicators were presented in order efficiency, accuracy and simple applicability of the proposed method.

variable-order fractional derivatives, Adams numerical scheme, Butterfly- Shaped Chaotic Attractor System, Robust Control