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.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Numerical methods in inverse problems
Numerical methods in engineering
Publication details
- Journal / source
- Gulf Journal of Mathematics
- Publisher
- Vertex Academic Press
- Volume
- 23
- Issue
- 2
- Publication date
- 20 July 2026