天津师范大学学报（自然科学版）2024，Vol.44Issue(1)：22-27,6.DOI:10.19638/j.issn1671-1114.20240103
奇异函数分数阶导数的Hadamard有限部分积分表示形式
Hadamard finite part integral representations for fractional derivatives of singular functions
摘要
Abstract
The Riemann-Liouville and Caputo fractional derivatives are studied for functions involving a singular point,and their Hadamard finite part integral representations are given.Then the representations are used to derive the Psi series expan-sions for the fractional derivatives about the origin,which accurately describe the singular behavior of the fractional derivatives.In addition,the representations can conveniently be used to calculate the fractional derivatives by using the high-accuracy al-gorithm evaluating the Hadamard finite part integrals.Finally,a Chebyshev spectral approximation method with singularity sep-aration is designed,and the correctness and effectiveness of the Hadamard representation of fractional derivative and its nu-merical algorithm are verified by numerical examples.关键词
奇异函数/分数阶导数/Hadamard有限部分积分/Chebyshev谱逼近Key words
singular function/fractional derivative/Hadamard finite part integral/Chebyshev spectral approximation分类
数理科学引用本文复制引用
娄汝馨,廉欢,王同科..奇异函数分数阶导数的Hadamard有限部分积分表示形式[J].天津师范大学学报（自然科学版）,2024,44(1):22-27,6.基金项目
国家自然科学基金资助项目(11971241) （11971241）
天津市高等学校创新团队培养计划资助项目(TD13-5078) （TD13-5078）
天津师范大学教学改革资助项目(JG01221074). （JG01221074）
