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Fractional Landweber Iterative Regularization Method for Identifying the Unknown Source of the Time-Fractional Diffusion Problem

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Abstract

In this paper, we study an inverse problem to determine an unknown source term in the time-fractional diffusion equation with variable coefficients in a general bound domain. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. We introduce the fractional Landweber iterative regularization method to solve inverse source problem. Based on an a conditional stability result, error convergent estimates between the exact solution and the regularization solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule are also given. Some numerical experiments prove that the fractional Landweber method provides better numerical result than the classical Landweber method under the same iterative steps.

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Authors and Affiliations

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

    Fan Yang, Jun-Liang Fu, Ping Fan & Xiao-Xiao Li

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  1. Fan Yang
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  2. Jun-Liang Fu
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  3. Ping Fan
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  4. Xiao-Xiao Li
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Correspondence to Fan Yang.

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The project is supported by the National Natural Science Foundation of China (No. 11961044), the Doctor Fund of Lan Zhou University of Technology, the Natural Science Foundation of Gansu Provice (No. 21JR7RA214).

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Yang, F., Fu, JL., Fan, P. et al. Fractional Landweber Iterative Regularization Method for Identifying the Unknown Source of the Time-Fractional Diffusion Problem. Acta Appl Math 175, 13 (2021). https://doi.org/10.1007/s10440-021-00442-1

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