Abstract
In this paper, we consider a time-fractional inverse diffusion problem, where the data are given at x=1 and the solution is required in the interval 0<x<1. This problem is typically ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. The simplified Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, a new a posteriori parameter choice rule is proposed and the Hölder type error estimate is also obtained. Some different type examples are presented to demonstrate the feasibility and efficiency of the proposed method.
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