Reconstruction of a Space-Time-Dependent Source in Subdiffusion Models via a Perturbation Approach

In this article we study two inverse problems of recovering a space-time-dependent source component from the lateral boundary observation in subdiffusion model. The mathematical model involves Djrbashian--Caputo fractional derivative order $\alpha\in(0,1)$ time, and second-order elliptic operator with time-dependent coefficients. We establish well-posedness conditional stability result for using novel perturbation argument refined regularity estimates associated direct problem. Further, present numerical algorithm efficiently accurately reconstructing component, provide several two-dimensional results showing feasibility recovery.