Numerical solution for Stokes' first problem for a heated generalized second grade fluid with fractional derivative

In this paper, we consider Stokes' first problem for a heated generalized second grade fluid with fractional derivative (SFP-HGSGF). An effective implicit numerical approximation scheme (INAS) for solving the SFP-HGSGF is presented. The stability and convergence of the numerical scheme are analyzed by the energy method. Some numerical examples are presented to show the application of the present technique. The numerical results exhibit the good performance of our theoretical analysis.