摘要：

This report focus on research results of time fractional Rayleigh-Stokes problem in a heated second grade fluid with initial condition. In virtue of the Galerkin method and some analysis skills, the existence, uniqueness and regularity of weak solutions are obtained when the order α of Riemann-Liouville derivative belongs to ½. Moreover, the improved regularity of weak solutions is established in the case that the regularity of the initial value condition and the source term improves.