Quasi-reversibility method to identify a space-dependent source for the time-fractional diffusion equation

In this study, we consider a problem of recovering a space-dependent source for the time-fractional diffusion equation, where the additional data is the observation at a final moment t=Tt=T. We develop a quasi-reversibility method to overcome the ill-posedness of the problem. The convergence estimates under an a priori parameter choice rule and an a posteriori parameter choice rule are proved, respectively. Finally, numerical examples are presented which demonstrate the effectiveness of the regularization methods and confirm the theoretical claims.