Startseite Mathematik Two regularization methods for identifying the source term of Caputo–Hadamard type time fractional diffusion-wave equation
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Two regularization methods for identifying the source term of Caputo–Hadamard type time fractional diffusion-wave equation

  • Fan Yang EMAIL logo , Ruo-Hong Li , Yin-Xia Gao und Xiao-Xiao Li
Veröffentlicht/Copyright: 9. April 2025

Abstract

In this paper, the inverse problem of source term identification for Caputo–Hadamard type time-fractional diffusion-wave equation is studied. Firstly, we prove that the problem is ill-posed, and give the optimal error bound and the conditional stability results. Secondly, we apply fractional Tikhonov regularization method and fractional Landweber iterative regularization method to solve the problem. Based on the conditional stability results, we give error estimates under the a priori regularization parameter selection rule and the a posteriori regularization parameter selection rule respectively. In addition, we give three numerical examples to prove the validity and feasibility of the selected regularization method. What is novel is that we apply L21 formula, Crank–Nicolson format and the finite difference method to discrete equation.

MSC 2020: 35R25; 47A52; 35R30

Award Identifier / Grant number: 12461083

Funding statement: The project is supported by the National Natural Science Foundation of China (No. 12461083) and the Doctor Fund of Lan Zhou University of Technology.

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Received: 2024-07-21
Revised: 2025-02-16
Accepted: 2025-02-28
Published Online: 2025-04-09
Published in Print: 2025-06-01

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