An improved tau method for the multi-dimensional fractional Rayleigh-Stokes problem for a heated generalized second grade fluid

We develop efficient algorithms based on the Legendre-tau approximation for one- and two-dimensional fractional Rayleigh-Stokes problems for a generalized second-grade fluid. The time fractional derivative is described in the Riemann-Liouville sense. Discussions on the L2-convergence of the proposed method are presented. Numerical results for one- and two-dimensional examples with smooth and nonsmooth solutions are provided to verify the validity of the theoretical analysis, and to illustrate the efficiency of the proposed algorithms.