A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional Derivative

In this paper, we investigate the regularization of the backward problem for a diffusion process with a time-fractional derivative. We propose a novel double-parameter regularization scheme that integrates the quasi-reversibility method for the governing equation with the quasi-boundary method. Theoretical analysis establishes the regularity and the convergence analysis of the regularized solution, along with a convergence rate under an a-priori regularization parameter choice rule in the general-dimensional case. Finally, numerical experiments validate the effectiveness of the proposed scheme.