In this paper, two kinds of stochastic differential equations with piecewise constant arguments are investigated. Sufficient conditions for the existence of the square-mean S-asymptotically $\omega$-periodic solutions of these two type equations are derived where $\omega$ is an integer. Then, the global asymptotic stability for one of them is considered by using the comparative approach. In order to show the theoretical results, we give two examples.

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.