Identifying a fractional order and a space source term in a time-fractional diffusion-wave equation simultaneously

This paper is devoted to identify simultaneously a fractional order and a space source term in a multi-dimensional time-fractional diffusion-wave equation by the final time measurement data. We prove the uniqueness and stability of the inverse problem. Then we use the Levenberg–Marquardt method to recover the fractional order and the space source term simultaneously, and propose a finite dimensional approximation algorithm based on the linear finite element basis to find a regularized solution. Numerical examples in one-dimensional and two-dimensional cases are provided to illustrate the efficiency of the proposed algorithm.