Two regularization methods for identifying the unknown source term of space-time fractional diffusion-wave equation

In this paper, the inverse problem of identifying the unknown source for the space-time fractional diffusion-wave equation is researched. This problem is ill-posed and needs the regularization approach to solve this inverse problem. The fractional Tikhonov regularization method and the quasi-inverse regularization method are used to obtain the fractional Tikhonov regularization solution and the quasi-inverse regularization solution, respectively. Under the a priori and the a posteriori regularization parameter selection rules, the error estimates of the regularization solutions and the exact solution are given. Finally, we provide several numerical examples to show the effectiveness of the approach.