Conditional stability and regularization method for inverse source for distributed order time-fractional diffusion equation

This article is concerned with the problem of source identification for a distributed-order time-fractional diffusion equation (DTFDE). The uniqueness, ill-posedness and conditional stability estimate for the inverse source problem are demonstrated. Our main objective is to reconstruct the stable source term utilizing an iterative generalized quasi-reversibility method(IGQRM). In theory, an a priori and an a posteriori regularization parameter selection strategies are proposed to obtain the convergence estimates between the regularized solution and the exact solution. In numerical experiment, some numerical examples are presented to describe the stability and validity of our proposed regularization method.