Inverse source problem for time-fractional diffusion with discrete random noise

Abstract

In this paper, we deal with the inverse source 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 does not depend continuously on the data. To regularize the unstable solution, we use the trigonometric method in nonparametric regression associated with the truncated expansion method. We also investigate the convergence rate.