On a backward problem for inhomogeneous time-fractional diffusion equations

Abstract

In this paper, we consider a final value problem for time-fractional diffusion equation with inhomogeneous source. The main goal of our paper is to determine an approximated initial data from the observation data at final time by constructing a regularized solution using a mollification method. Under appropriate regularity assumptions of the exact solution, we give convergence rate between the reconstructed solution and the exact one. We also provide a numerical example to illustrate the main results.