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

摘要

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.