Stochastic Impulsive Fractional Differential Evolution Equations with Infinite Delay

Abstract

In this paper, we investigate a class of stochastic impulsive fractional differential evolution equations with infinite delay in Banach space. Firstly, sufficient conditions of the existence and uniqueness of the mild solution for this type of equations are derived by means of the successive approximation.  Then we use the Bihari's inequality to get the stability in mean square of the mild solution. Finally, an example is presented to illustrate the results.