The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation

In this paper, we identify the initial value for a time-fractional diffusion equation on a columnar axis-symmetric domain. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the domain. Two different kinds of fractional Tikhonov methods are used to solve this problem. Under the a priori and the a posteriori regularization parameter choice rules, the error estimates between the regularization solutions and the exact solution are obtained, respectively. Different numerical examples are presented to illustrate the validity and effectiveness of our methods. (C) 2020 Elsevier B.V. All rights reserved.