Robin coefficient determination problem in a fractional parabolic differential equation

This article discusses the identification of an unknown Robin coefficient in a fractional parabolic equation using a noisy measurement of the ultimate solution over time. The problem is quite complex, involving a nonlocal, nonlinear, and ill-posed operator. To solve this problem, the article proposes a regularized optimization approach that minimizes a least-squares cost function. The article also examines the various conceptual and real-world challenges associated with this problem. The article demonstrates the presence of a singular and stable solution for the optimization problem. It utilizes the Morozov discrepancy principle and the conjugate gradient method to streamline the iterative reconstruction process. The proposed method is accurate and efficient, as several numerical examples demonstrate.