ON INITIAL VALUE AND TERMINAL VALUE PROBLEMS FOR SUBDIFFUSIVE STOCHASTIC RAYLEIGH-STOKES EQUATION

In this paper, we study two stochastic problems for time-fractional Rayleigh-Stokes 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.

Automated summary

This paper investigates two stochastic problems for time-fractional Rayleigh-Stokes equation, providing existence results and regularity properties for the mild solution of each problem using specific techniques.