Identify the fractional order and diffusion coefficient in a fractional diffusion wave equation

This paper is devoted to identifying the fractional order and diffusion coefficient in a time fractional diffusion wave equation from boundary observation data in one dimensional case. The uniqueness of recovering the fractional order and diffusion coefficient simultaneously has been proved by the Laplace transform and Gel’fand-Levitan theory. In addition, we apply the iterative regularizing ensemble Kalman method to provide a numerical implementation of the considered inverse problem. Four numerical examples are carried out to demonstrate the performance of the proposed method.