A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation

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$A fractional Tikhonov regul...$

A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation

Xiong, Xiangtuan; Xue, Xuemin

Applied mathematics and computation, 05/2019, Volume: 349

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In this paper, we are concerned with an inverse source problem for the time-fractional diffusion equation with variable coefficients in a general bounded domain. The problem is mildly ill-posed. A new fractional Tikhonov method is proposed. We discuss the a-priori regularization parameter choice rule and the a-posteriori regularization parameter choice rule, and prove the corresponding convergence estimates. Numerical experiments are conducted for illustrating effectiveness of the proposed method.

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