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Identifying the source term and the initial value simultaneously for Caputo–Hadamard fractional diffusion equation on spherically symmetric domain

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Abstract

In this paper, we consider the inverse problem for identifying the source term and initial value for time-fractional diffusion equation on spherically symmetric domain with Caputo–Hadamard fractional derivative. By solving the direct problem, the exact solutions of the problem can be calculated, and based on the expressions of the exact solutions, it can be analyzed that this problem is ill-posed. To address this, we employ the fractional Landweber iterative regularization method to restore the stability of the solutions. Furthermore, the error estimates under the priori regularization parameter choice rules and the posteriori regularization parameter choice rules are given, respectively. Finally, different numerical examples are presented to demonstrate the validity and effectiveness of our method.

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Funding

The project is supported by the National Natural Science Foundation of China (No.11961044), and the Natural Science Foundation of Gansu Province (No. 21JR7RA214).

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Authors and Affiliations

  1. School of Science, Lanzhou University of Technology, Lanzhou, 730050, Gansu, People’s Republic of China

    Chen-Yu Zhang, Fan Yang & Xiao-Xiao Li

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  1. Chen-Yu Zhang
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  2. Fan Yang
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  3. Xiao-Xiao Li
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The main idea of the article is given by Chen-Yu Zhang and Fan Yang. We confirmed the steps of the article. This view is shared by all the authors.

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Correspondence to Fan Yang.

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Communicated by Vinicius Albani.

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Zhang, CY., Yang, F. & Li, XX. Identifying the source term and the initial value simultaneously for Caputo–Hadamard fractional diffusion equation on spherically symmetric domain. Comp. Appl. Math. 43, 161 (2024). https://doi.org/10.1007/s40314-024-02679-6

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  • DOI: https://doi.org/10.1007/s40314-024-02679-6

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