Abstract
The purpose of this paper is to analyse the Rayleigh-Stokes problem for a heated generalized second-grade fluid with Riemann-Liouville fractional derivative. By virtue of the Galerkin method, the existence, uniqueness and regularity of weak solutions in L-infinity(0, b; L-2 (Omega)) boolean AND L-2 (0, b; H-0(1) (Omega)) of the proposed problem are obtained. Furthermore, we prove an improved regularity result of weak solutions in the case of h is an element of H-2 (Omega) and f is an element of L-2 (0 ,b; L-2(Omega)).