Regularized solution of an inverse source problem for a time fractional diffusion equation

In this paper, we study on an inverse problem to determine an unknown source term in a time fractional diffusion equation, whereby the data are obtained at the later time. In general, this problem is illposed, therefore the Tikhonov regularization method is proposed to solve the problem. In the theoretical results, a priori error estimate between the exact solution and its regularized solutions is obtained. We also propose two methods, a priori and a posteriori parameter choice rules, to estimate the convergence rate of the regularized methods. In addition, the proposed regularized methods have been verified by numerical experiments to estimate the errors between the regularized solutions and exact solutions. Eventually, from the numerical results it shows that the posteriori parameter choice rule method converges to the exact solution faster than the priori parameter choice rule method.