Identification of the zeroth‐order coefficient and fractional order in a time‐fractional reaction‐diffusion‐wave equation

Abstract

In this paper, we investigate an inverse problem of recovering the zeroth‐order coefficient and fractional order simultaneously in a time‐fractional reaction‐diffusion‐wave equation by using boundary measurement data from both of uniqueness and numerical method. We prove the uniqueness of the considered inverse problem and the Lipschitz continuity of the forward operator. Then the inverse problem is formulated into a variational problem by the Tikhonov‐type regularization. Based on the continuity of the forward operator, we prove that the minimizer of the Tikhonov‐type functional exists and converges to the exact solution under an a priori choice of regularization parameter. The steepest descent method combined with Nesterov acceleration is adopted to solve the variational problem. Three numerical examples are presented to support the efficiency and rationality of our proposed method.