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. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper focuses on identifying the fractional order and diffusion coefficient in a one-dimensional time fractional diffusion wave equation from boundary observation data. The uniqueness of recovering both parameters simultaneously is proved through Laplace transform and Gel'fand-Levitan theory. The study also presents a numerical implementation using the iterative regularizing ensemble Kalman method, with four numerical examples demonstrating the method's performance.