Square-mean S-asymptotically $\omega$-periodic solution for a stochastic fractional evolution equation driven by L\'{e}vy noise with piecewise constant argument

Abstract

In this paper, we introduce some concepts of square-mean S-asymptotically $\omega$-periodic stochastic processes. Using the stochastic analysis method and the Banach contraction mapping principle, we establish the existence and uniqueness results of the mild solution and the square-mean S-asymptotically $\omega$-periodic solution for a semilinear nonautonomous stochastic fractional evolution equation driven by L\'{e}vy noise.