Simultaneous Identification Of The Order And Spatial Source Term In A Time-fractional Diffusion Wave Equation

In this paper,we investigate the simultaneous identification problem of the order and space-dependent source term in a time fractional diffusion wave equation by using the data in a subdomain.We prove the uniqueness of the inverse problem and the Lipschitz continuity of the forward operator.We use the Tikhonov regularization method to transform the inverse problem into a variational problem,and prove that the minimizer of the Tikhonov type functional exists and converges to the exact solution under an a priori choice of the regularization parameter.Finally,we propose an accelerated steepest descent method to solve the variational problem,and verify the effectiveness of this method through three one-dimensional numerical examples.