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Two Regularization Methods for Identifying the Initial Value of Time-Fractional Telegraph Equation

  • Ying-Qing Liang , Fan Yang EMAIL logo and Xiao-Xiao Li
Published/Copyright: January 15, 2025

Abstract

In this article, an inverse problem for identifying the initial value of time-fractional telegraph equation is addressed. This is a typical ill-posed problem, meaning the solution does not depend continuously on the data. Besides, we give the conditional stability result based on an a priori bound condition. We utilize the modified quasi-boundary regularization method and the Landweber iterative regularization method to obtain the corresponding approximate solutions, respectively. The convergent error estimates under the a priori regularization parameter selection rule and the a posteriori regularization parameter selection rule are given. Some numerical experiments testify the effectiveness and precision of the proposed methods.

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.

  1. Author Contributions: T

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Received: 2024-10-05
Revised: 2024-12-01
Accepted: 2024-12-04
Published Online: 2025-01-15

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