An inverse potential problem for subdiffusion: stability and reconstruction

In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order α ∈ (0, 1) in time, from the terminal data. We prove that the inverse problem is locally Lipschitz for small terminal time, under certain conditions on the initial data. This result extends the result in [6] for the standard parabolic case to the fractional case. The analysis relies on refined properties of two-parameter Mittag-Leffler functions, e.g., complete monotonicity and asymptotics. Further, we develop an efficient and easy-to-implement algorithm for numerically recovering the coefficient based on (preconditioned) fixed point iteration and Anderson acceleration. The efficiency and accuracy of the algorithm is illustrated with several numerical examples.