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 αof Riemann-Liouville derivative belongs to½. 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.