Averaging Principle for a Class of Time-Fractal-Fractional Stochastic Differential Equations

Abstract

In this paper, we study a class of time-fractal-fractional stochastic differential equations with the fractal–fractional differential operator of Atangana under the meaning of Caputo and with a kernel of the power law type. We first establish the Hölder continuity of the solution of the equation. Then, under certain averaging conditions, we show that the solutions of original equations can be approximated by the solutions of the associated averaged equations in the sense of the mean square convergence. As an application, we provide an example with numerical simulations to explore the established averaging principle.