Square-mean S-asymptotically $ω$-periodic solution for a stochastic fractional evolution equation driven by Lévy noise with piecewise constant argument

In this paper, we introduce some concepts of square-mean S-asymptotically $ω$-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 $ω$-periodic solution for a semilinear nonautonomous stochastic fractional evolution equation driven by Lévy noise.

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