On a fractional Rayleigh–Stokes equation driven by fractional Brownian motion

In this work, a stochastic Rayleigh–Stokes equation driven by fractional Brownian motion is considered in both cases h∈0,12 and h∈12,1. The existence and uniqueness of mild solution in each case are established separately by applying a standard method that is Banach fixed point theorem. The required results are obtained by stochastic analysis techniques, fractional calculus. In addition, the regularity results of mild solution for this problem is investigated.