An Averaging Limit Theorem for Impulsive Delay Stochastic Fractional Differential Equations

Abstract

In this article, we present an averaging limit theorem for impulsive delay Caputo fractional stochastic differential equations. In contrast to the present literature, a new technique is adopted to overcome the difficulties hired by the impulsive term based on impulsive-type Grönwall inequality. As a result, it is proved that the solution of the non-impulsive averaged delay Caputo fractional stochastic differential equations converges to that of the standard impulsive delay Caputo fractional stochastic differential equations in L^q-sense. Finally, an example is constructed to enhance the analytical result.