Numerical analysis of the Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives

In this paper, we consider numerical analysis of the Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. The explicit and the implicit finite difference method are presented. Their stability and convergence are discussed via new technique of Fourier analysis. The solvability of the implicit finite difference method is also analyzed. The theoretical results are verified by a numerical example.