A NUMERICAL APPROACH FOR THE FRACTIONAL STOKES EQUATIONS WITH CAPUTO DERIVATIVE

As is widely known, fractional derivatives are a powerful tool for describing anomalous diffusion phenomena. This article presents a numerical investigation of a class of Caputo-type Stokes model, where the order of the time-fractional derivative is alpha is an element of (0, 1). The numerical solution of this model is obtained by combining the L2-1(sigma) formula in time with the Taylor-Hood mixed finite element approximation in space. The stability of the velocity field in the L-2- norm and the optimal error estimate are demonstrated, and numerical examples are provided to validate the theoretical analysis. Finally, the influences of varying a on the solution of the considered model are discussed, and a comparison with integer-order model is performed.