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.

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