A Numerical Analysis for Solving the Time-Fractional Cattaneo Model Involving the Riesz Space-Fractional Derivative

This manuscript presents an efficient hybrid numerical method for solving one- and two-dimensional time-fractional Cattaneo models that incorporate the Riesz space-fractional derivative. The proposed approach combines the Crank–Nicolson scheme for temporal discretization with the classical Galerkin finite element method for spatial discretization. The stability of the semi-discrete scheme is established in the L2 norm, and a convergence analysis of the fully discrete scheme is carried out, yielding a temporal convergence order of O(Δt)3−μ and a spatial convergence order of O(R2). Finally, two numerical examples, in one and two dimensions, are provided to demonstrate the accuracy and efficiency of the proposed method and to verify the theoretical findings.