An Order Reduction Method for the Nonlinear Caputo-Hadamard Fractional Diffusion-Wave Model

doi:10.1007/s42967-023-00295-5

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (1): 392-408.doi: 10.1007/s42967-023-00295-5

• ORIGINAL PAPERS • 上一篇

An Order Reduction Method for the Nonlinear Caputo-Hadamard Fractional Diffusion-Wave Model

Jieying Zhang¹, Caixia Ou¹, Zhibo Wang¹, Seakweng Vong²

1 School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510006, Guangdong, China;
2 Department of Mathematics, University of Macau, Macao 999078, China

收稿日期:2023-03-06 修回日期:2023-06-02 接受日期:2023-06-29 出版日期:2025-04-21 发布日期:2025-04-21
通讯作者: Zhibo Wang,wzbmath@gdut.edu.cn;Jieying Zhang,zjy529@icloud.com;Caixia Ou,oucaixiaywxk@163.com;Seakweng Vong,swvong@um.edu.mo E-mail:wzbmath@gdut.edu.cn;zjy529@icloud.com;oucaixiaywxk@163.com;swvong@um.edu.mo
基金资助:
This research is supported by the National Natural Science Foundation of China (No. 11701103), the Natural Science Foundation of Guangdong Province of China (Nos. 2022A1515012147, 2023A1515011504), and University of Macau (File Nos. MYRG2020-00035-FST, MYRG2018-00047-FST).

An Order Reduction Method for the Nonlinear Caputo-Hadamard Fractional Diffusion-Wave Model

Jieying Zhang¹, Caixia Ou¹, Zhibo Wang¹, Seakweng Vong²

1 School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510006, Guangdong, China;
2 Department of Mathematics, University of Macau, Macao 999078, China

Received:2023-03-06 Revised:2023-06-02 Accepted:2023-06-29 Online:2025-04-21 Published:2025-04-21
Supported by:
This research is supported by the National Natural Science Foundation of China (No. 11701103), the Natural Science Foundation of Guangdong Province of China (Nos. 2022A1515012147, 2023A1515011504), and University of Macau (File Nos. MYRG2020-00035-FST, MYRG2018-00047-FST).

摘要/Abstract

摘要： In this paper, the numerical solutions of the nonlinear Hadamard fractional diffusion-wave model with the initial singularity are investigated. Firstly, the model is transformed into coupled equations by virtue of a symmetric fractional-order reduction method. Then the L_log,2-1_σ formula on nonuniform grids is applied to approach to the time fractional derivative. In addition, the discrete fractional Grönwall inequality is used to analyze the optimal convergence of the constructed numerical scheme by the energy method. The accuracy of the theoretical analysis will be demonstrated by means of a numerical experiment at the end.

关键词: Caputo-Hadamard fractional differential equations (FDEs), Symmetric fractional-order reduction method, Nonuniform mesh, Stability and convergence

Abstract: In this paper, the numerical solutions of the nonlinear Hadamard fractional diffusion-wave model with the initial singularity are investigated. Firstly, the model is transformed into coupled equations by virtue of a symmetric fractional-order reduction method. Then the L_log,2-1_σ formula on nonuniform grids is applied to approach to the time fractional derivative. In addition, the discrete fractional Grönwall inequality is used to analyze the optimal convergence of the constructed numerical scheme by the energy method. The accuracy of the theoretical analysis will be demonstrated by means of a numerical experiment at the end.

Key words: Caputo-Hadamard fractional differential equations (FDEs), Symmetric fractional-order reduction method, Nonuniform mesh, Stability and convergence

中图分类号:

Jieying Zhang, Caixia Ou, Zhibo Wang, Seakweng Vong. An Order Reduction Method for the Nonlinear Caputo-Hadamard Fractional Diffusion-Wave Model[J]. Communications on Applied Mathematics and Computation, 2025, 7(1): 392-408.

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An Order Reduction Method for the Nonlinear Caputo-Hadamard Fractional Diffusion-Wave Model

An Order Reduction Method for the Nonlinear Caputo-Hadamard Fractional Diffusion-Wave Model

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