On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag-Leffler kernel

The purpose of this paper is to study the existence and uniqueness of the solution of nonlinear fractional differential equations with Mittag-Leffler nonsingular kernel. Two numerical methods to solve this problem are designed, and their stability and error estimates are investigated by discretizing the convolution integral and using the Gronwall's inequality. Finally, the theoretical results are verified by using five illustrative examples.