Abstract
In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on the solution in the frequency domain. Convergence estimates are presented under the a priori bound assumptions for the exact solution. We also provide a numerical example to illustrate our results.