Inverse Source Reconstruction with L1 Fractional Method

Abstract

This paper studies an inverse source identification problem for a diffusion model with a time-fractional derivative under Dirichlet boundary conditions. We establish the differentiability of the unknown source and prove the injectivity of the associated input–output mapping, thereby guaranteeing the uniqueness of the reconstruction. A numerical procedure based on an L1 finite-difference approximation is developed to stably compute the source term. Several numerical experiments demonstrate the accuracy and robustness of the proposed approach. computational efficiency are also discussed.