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

TL;DR

This paper introduces the concept of square-mean S-asymptotically ω-periodic stochastic processes and proves the existence and uniqueness of such solutions for a class of stochastic fractional evolution equations driven by Lévy noise.

Contribution

It extends the theory of periodic solutions to stochastic fractional equations with Lévy noise by defining new process classes and establishing their solution properties.

Findings

Existence of mild solutions for the stochastic fractional evolution equation.

Uniqueness of the square-mean S-asymptotically ω-periodic solutions.

Application of Banach contraction principle in stochastic setting.

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.