Exact solution of a class of fractional integro-differential equations with the weakly singular kernel based on a new fractional reproducing kernel space

被引：19

作者：

Chen, Zhong ^{[1
]}

Wu, Longbin ^{[1
]}

Lin, Yingzhen ^{[2
]}

机构：

[1] Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Shandong, Peoples R China

[2] Beijing Inst Technol, Sch Sci, Zhuhai Campus, Zhuhai 519088, Guangdong, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 10期

基金：

中国国家自然科学基金;

关键词：

fractional integro-differential equation; fractional reproducing kernel space; weakly singular kernel; COLLOCATION METHOD; ORDER;

D O I：

10.1002/mma.4870

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct a new fractional weighted reproducing kernel space, which is the minimum space containing the exact solution. The closed form of the reproducing kernel is obtained. Using this fractional reproducing kernel space, a class of fractional integro-differential equations with a weakly singular kernel is solved. The error estimation is given. The final numerical experiments demonstrate the correctness of the theory and the effectiveness of the method.

引用

页码：3841 / 3855

页数：15

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