A FRACTIONAL LANDWEBER ITERATION METHOD FOR SIMULTANEOUS INVERSION IN A TIME-FRACTIONAL DIFFUSION EQUATION

Jin Wen; Chong-Wang Yue; Zhuan-Xia Liu; Donal O'Regan

doi:10.11948/20230051

2023 Volume 13 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(6): 3374-3402

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Jin Wen, Chong-Wang Yue, Zhuan-Xia Liu, Donal O'Regan. A FRACTIONAL LANDWEBER ITERATION METHOD FOR SIMULTANEOUS INVERSION IN A TIME-FRACTIONAL DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3374-3402. doi: 10.11948/20230051

Citation:

Jin Wen, Chong-Wang Yue, Zhuan-Xia Liu, Donal O'Regan. A FRACTIONAL LANDWEBER ITERATION METHOD FOR SIMULTANEOUS INVERSION IN A TIME-FRACTIONAL DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3374-3402. doi: 10.11948/20230051

A FRACTIONAL LANDWEBER ITERATION METHOD FOR SIMULTANEOUS INVERSION IN A TIME-FRACTIONAL DIFFUSION EQUATION

1.
Department of Mathematics, Northwest Normal University, Gansu 730070, China
2.
School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland

Author Bio: Email: yuechongwangsd@163.com(C. Yue); Email: liu11200810@163.com(Z. Liu); Email: donal.oregan@nuigalway.ie(D. O'Regan)
Corresponding author: Email: wenj@nwnu.edu.cn/wenjin0421@163.com(J. Wen)
Fund Project: The authors were supported by the NNSF of China (12261082, 11326234), NSF of Gansu Province (145RJZA099), Scientific research project of Higher School in Gansu Province (2014A-012), and Project of NWNU-LKQN2020-08

Abstract

Abstract

In the present paper, we study the problem to identify the space-dependent source term and initial value simultaneously for a time-fractional diffusion equation. This inverse problem is ill-posed, and we use the idea of decoupling to turn it into two operator equations based on the Fourier method. To solve the inverse problem, a fractional Landweber regularization method is proposed. Furthermore, we present convergence estimates between the exact solution and the regularized solution by using the a-priori and the a-posteriori parameter choice rules. In order to verify the accuracy and efficiency of the proposed method, several numerical examples are constructed.
- Time-fractional diffusion equation /
- simultaneous inversion /
- fractional Landweber iteration /
- a-priori and a-posteriori regularization parameters
MSC: 41A28, 65N21, 35R11

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References

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