Abstract
This paper is concerned with the problem of identifying the space-dependent source term and initial value simultaneously for a time-fractional diffusion equation. The inverse problem is ill-posed, and the idea of decoupling it into two operator equations is applied. In order to solve this inverse problem, a fractional Tikhonov regularization method is proposed. Furthermore, the corresponding convergence estimates are presented by using the a priori and a posteriori parameter choice rules. Several numerical examples compared with the classical Tikhonov regularization are constructed for verifying the accuracy and efficiency of the proposed method.
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