Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian

Abstract

In this paper, we consider a time-fractional backward problem with a fractional Laplacian. We propose a fractional Tikhonov regularization method for solving this problem under the the a-priori parameter choice rule. Error estimates are proved. Some numerical examples are shown to verify the effectiveness of the proposed method.