Regularization of Ill-Posed Problem for Evolution Equation with Nonlocal Operator

The paper deals with the ill-posedness of the backward problem for fractional evolution equation. The main contribution of our paper is to construct the regularized solution using the Fourier truncation method. We also derive estimates between the regularized solution and the sought solution. Error estimates are obtained in \(L^2\) and Hilbert space scales \(\mathbb H^\mu\). Our main analysis is based on the estimation of the Mittag-Leffler functions. To the best of the author's knowledge, there are not any results for focusing the regularization of backward problem for elliptic equations with nonlocal operator.