Spectral approximations to the fractional integral and derivative

被引：137

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

共 50 条

[1] Spectral approximations to the fractional integral and derivative
Changpin Li
Fanhai Zeng
Fawang Liu
[J]. Fractional Calculus and Applied Analysis, 2012, 15 : 383 - 406
[2] Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations
Yuri Dimitrov
[J]. Communications on Applied Mathematics and Computation, 2021, 3 : 545 - 569
[3] Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations
Dimitrov, Yuri
[J]. COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2021, 3 (03) : 545 - 569
[4] Nabla Fractional Derivative and Fractional Integral on Time Scales
Gogoi, Bikash
Saha, Utpal Kumar
Hazarika, Bipan
Torres, Delfim F. M.
Ahmad, Hijaz
[J]. AXIOMS, 2021, 10 (04)
[5] Fractional Modified Dyadic Integral and Derivative on ℝ+
B. I. Golubov
[J]. Functional Analysis and Its Applications, 2005, 39 : 135 - 139
[6] Generalized fractional Hilfer integral and derivative
Valdes, Juan E. Napoles
[J]. CONTRIBUTIONS TO MATHEMATICS, 2020, 2 : 55 - 60
[7] Modified Dyadic Integral and Fractional Derivative on ℝ+
B. I. Golubov
[J]. Mathematical Notes, 2006, 79 : 196 - 214
[8] Constructions of Second Order Approximations of the Caputo Fractional Derivative
Apostolov, Stoyan
Dimitrov, Yuri
Todorov, Venelin
[J]. LARGE-SCALE SCIENTIFIC COMPUTING (LSSC 2021), 2022, 13127 : 31 - 39
[9] Asymptotic approximations for systems incorporating fractional derivative damping
Liebst, BS
Torvik, PJ
[J]. JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 1996, 118 (03): : 572 - 579
[10] Finite approximations of a discrete-time fractional derivative
Stanislawski, Rafal
Hunek, Wojciech P.
Latawiec, Krzysztof J.
[J]. 2011 16TH INTERNATIONAL CONFERENCE ON METHODS AND MODELS IN AUTOMATION AND ROBOTICS, 2011, : 142 - 145

← 1 2 3 4 5 →