Identification and regularization for unknown source for a time-fractional diffusion equation

In this paper, we consider the inverse problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. Using the method of truncated integration and the Fourier transform, we construct regularized solutions and derive explicitly error estimate. Two numerical examples are presented to illustrate the validity and effectiveness of our method.