A Residual Power Series Method for Time-Fractional Stokes Equations

Abstract

This paper presents a residual power series method for solving the time-fractional Stokes equations. The approach combines Chebyshev collocation for spatial discretization with RPSM for temporal evolution. We establish theoretical convergence properties and validate the RPSM temporal convergence through numerical experiments. The spatial discretization leads to a mixed formulation with saddle-point structure and mean-zero pressure constraint. Numerical results show geometric convergence of the temporal series. These results demonstrate that the proposed method is a practical tool for time-fractional incompressible flow simulations.