Abstract
Abstract
This study investigates the solution of generalized second-order fractional Stokes equations through the application of a centroid interpolation collocation method. These equations serve as fundamental models in the field of complex fluid dynamics, with significant applications in areas such as viscoelastic fluid mechanics, porous media flow, and biomedical engineering. The proposed meshless barycentric interpolation collocation method (MBICM) eliminates the need for domain meshing, thereby enabling efficient and accurate numerical approximations on irregular domains. The governing equations are formulated based on the Caputo definition of time fractional derivatives, and the discrete matrix system is constructed using barycentric interpolation basis functions. The stability of the method is theoretically analyzed through Lebesgue constant estimation and error bound analysis. Numerical experiments, including linear biharmonic problems and two-dimensional fractional Stokes equations, are conducted to demonstrate the accuracy and effectiveness of the proposed approach.