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Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator

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Abstract

In this paper, we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator. First, we prove that this inverse problem is ill-posed, and give the conditional stability. Then, we give the optimal error bound for this inverse problem. Next, we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem, and give corresponding error estimates under different regularization parameter selection rules. Finally, we verify the effectiveness of the method through numerical examples.

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou University of Technology, Lanzhou, 730000, China

    Fan Yang, Qiaoxi Sun & Xiaoxiao Li

Authors
  1. Fan Yang
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  2. Qiaoxi Sun
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  3. Xiaoxiao Li
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Corresponding author

Correspondence to Fan Yang.

Additional information

The project is supported by the National Natural Science Foundation of China (11961044), the Doctor Fund of Lan Zhou University of Technology, and the Natural Science Foundation of Gansu Provice (21JR7RA214).

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Yang, F., Sun, Q. & Li, X. Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator. Acta Math Sci 42, 1485–1518 (2022). https://doi.org/10.1007/s10473-022-0412-5

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  • DOI: https://doi.org/10.1007/s10473-022-0412-5

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