A New Approximate Analytical Method and its Convergence for Fuzzy Time-Fractional Advection-Diffusion Equations

This article introduces a new numerical approach based on the Laplace Homotopy Perturbation Method (LHPM) to solve the one-dimensional Fuzzy Time-Fractional Advection-Diffusion Equation (FTFADE) in the Caputo sense, considering fuzzy initial conditions. The proposed method demonstrates how fuzzy numerical solutions gradually converge to precise ones, supported by clear illustrative examples. We also establish sufficient conditions that guarantee the uniqueness of the solution and analyze the convergence of the method. Moreover, we compare fuzzy solutions for different uncertainty levels and fractional orders to provide a deeper understanding of the model’s behavior. The results are presented graphically to highlight the accuracy, efficiency, and reliability of the proposed method.