On initial value and terminal value problems for subdiffusive stochastic Rayleigh-Stokes equation

Abstract

In this paper, we study two stochastic problems for time-fractional RayleighStokes equation including the initial value problem and the terminal value problem. Here, two problems are perturbed by Wiener process, the fractional derivative are taken in the sense of Riemann-Liouville, the source function and the time-spatial noise are nonlinear and satisfy the globally Lipschitz conditions. We attempt to give some existence results and regularity properties for the mild solution of each problem.