Spectral approximations to the fractional integral and derivative

被引：143

作者：

Li, Changpin ^{[1
]}

Zeng, Fanhai ^{[1
]}

Liu, Fawang ^{[2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2012年 / 15卷 / 03期

基金：

中国国家自然科学基金;

关键词：

fractional integral; Caputo derivative; spectral approximation; Jacobi polynomials; DIFFERENTIAL-EQUATIONS; DIFFUSION EQUATIONS; ALGORITHMS; CALCULUS; SYSTEMS;

D O I：

10.2478/s13540-012-0028-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

引用

页码：383 / 406

页数：24

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