Computational Methods for Time-Fractional Differential Equations

In this study, we propose and analyze a finite difference scheme for solving time-fractional partial differential equations with Caputo derivatives. Such equations effectively model physical phenomena with memory and hereditary properties, including anomalous diffusion and viscoelastic behavior. The method is based on time and space discretization, and its stability is rigorously established via von Neumann analysis. The derived conditions confirm the robustness of the scheme under suitable discretization. To evaluate its accuracy, numerical results are compared with the exact solution, showing excellent agreement through detailed error analysis. Simulations are conducted in MATLAB, with results summarized in tables and figures. The proposed scheme offers a reliable computational framework with broad applicability in science and engineering.