An optimal method for fractional heat conduction problem backward in time

Abstract

In this article, we consider a fractional order backward heat conduction problem in two-dimensional space which is associated with a deblurring problem. The problem is seriously ill-posed. We propose an optimal regularization method to solve the problem in the presence of noisy data, and obtain the optimal stability error estimation. A deblurring and denoising experiment shows that the optimal method is comparable with the Tikhonov method.