Spectral approximations to the fractional integral and derivative

被引：145

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 32 条

[21] Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results [J].

Rossikhin, Yuriy A. ;

Shitikova, Marina V. .

APPLIED MECHANICS REVIEWS, 2010, 63 (01) :1-52

[22] A new operational matrix for solving fractional-order differential equations [J].

Saadatmandi, Abbas ;

Dehghan, Mehdi .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (03) :1326-1336

[23]

Samko S. G., 1993, Fractional Integrals and Derivatives, DOI DOI 10.1007/S10957-022-02125-9

[24] On the numerical evaluation of fractional derivatives in multi-degree-of-freedom systems [J].

Schmidt, Andre ;

Gaul, Lothar .

SIGNAL PROCESSING, 2006, 86 (10) :2592-2601

[25]

Shen J., 2011, Spectral Methods, DOI DOI 10.1007/978-3-540-71041-7

[26]

Sousa E., 2010, P FDA 10 4 IFAC WORK

[27] Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives [J].

Sugiura, Hiroshi ;

Hasegawa, Takemitsu .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 223 (01) :459-468

[28] FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION [J].

Sun, Hongguang ;

Chen, Wen ;

Li, Changpin ;

Chen, Yangquan .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (04)

[29] A fully discrete difference scheme for a diffusion-wave system [J].

Sun, ZZ ;

Wu, XN .

APPLIED NUMERICAL MATHEMATICS, 2006, 56 (02) :193-209

[30] ON THE APPEARANCE OF THE FRACTIONAL DERIVATIVE IN THE BEHAVIOR OF REAL MATERIALS [J].

TORVIK, PJ ;

BAGLEY, RL .

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1984, 51 (02) :294-298

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