Square-Mean Pseudo $S$-Asymptotically $(ω, c)$-Periodic Mild Solutions to Some Stochastic Fractional Evolution Systems

Abstract

In this paper, we introduce the concept of square-mean pseudo $S$-asymptotically $(ω,c)$-periodic for stochastic processes and establish some composition and convolution theorems for such stochastic processes. In addition, we investigate the existence and uniqueness of square-mean pseudo $S$-asymptotically $(ω,c)$-periodic mild solutions to some stochastic fractional integrodifferential equations. We illustrate our main results with an application to stochastic Weyl fractional integrodifferential equations.