The quasi-reversibility regularization method for identifying the unknown source for time fractional diffusion equation

The inverse problem of determining the unknown source for a fractional diffusion equation is studied. This problem is ill-posed in the sense of Hadamard, i.e., small changes in the measured data can blow up the solution. The quasi-reversibility regularization method is applied to solve it. Convergence estimates are presented under an a priori parameter choice rule and an a posteriori parameter choice rule, respectively. Numerical examples are given to show that the regularization method is effective and stable.