A HIGH ORDER SCHEME FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO-HADAMARD DERIVATIVE

被引：1
|
作者：
Ye, Xingyang [1 ]
Cao, Junying [2 ]
Xu, Chuanju [3 ,4 ]
机构：
[1] Jimei Univ, Sch Sci, Xiamen 361021, Peoples R China
[2] Guizhou Minzu Univ, Sch Data Sci & Informat Engn, Guiyang 550025, Peoples R China
[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[4] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performan, Xiamen 361005, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL MATHEMATICS | 2025年 / 43卷 / 03期
关键词：
Caputo-Hadamard derivative; Fractional differential equations; High order scheme; Stability and convergence analysis; LOGARITHMIC CREEP LAW; DIFFUSION; MODEL;
D O I：
10.4208/jcm.2312-m2023-0098
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider numerical solutions of the fractional diffusion equation with the alpha order time fractional derivative defined in the Caputo-Hadamard sense. A high order time-stepping scheme is constructed, analyzed, and numerically validated. The contribution of the paper is twofold: 1) regularity of the solution to the underlying equation is investigated, 2) a rigorous stability and convergence analysis for the proposed scheme is performed, which shows that the proposed scheme is 3 + alpha order accurate. Several numerical examples are provided to verify the theoretical statement.
引用
收藏
页码：615 / 640
页数：26
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