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.

<abstract><p>In this paper, we introduce the concept of an S-asymptotically $ \omega $-periodic process in distribution for the first time, and by means of the successive approximation and the Banach contraction mapping principle, respectively, we obtain sufficient conditions for the existence and uniqueness of the S-asymptotically $ \omega $-periodic solutions in distribution for a class of stochastic fractional functional differential equations.</p></abstract>

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In this paper, we introduce the concepts of S-asymptotically ω-periodic solutions in distribution for a class of stochastic fractional functional differential equations. The existence and uniqueness results for the S-asymptotically ω-periodic solutions in distribution are obtained by means of the successive approximation and the Banach contraction mapping principle, respectively.

In this paper, we investigate a class of nonlinear impulsive stochastic differential evolution equations with infinite delay in Banach space. Based on the Krasnoselskii's fixed point theorem, sufficient conditions of the existence of the square mean piecewise almost periodic solutions to this type of equations are derived. Moreover, the exponential stability of the square mean piecewise almost periodic solution is investigated.