The operational matrix of fractional integration for shifted Chebyshev polynomials

被引：154

作者：

Bhrawy, A. H. ^{[1
,2
]}

Alofi, A. S. ^{[2
]}

机构：

[1] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf, Egypt

[2] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia

来源：

APPLIED MATHEMATICS LETTERS | 2013年 / 26卷 / 01期

关键词：

Operational matrix; Shifted Chebyshev polynomials; Tau method; Multi-term FDEs; Riemann-Liouville derivative; DIFFERENTIAL-EQUATIONS; SERIES APPROACH; IDENTIFICATION; ORDER; SYSTEM;

D O I：

10.1016/j.aml.2012.01.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new shifted Chebyshev operational matrix (SCOM) of fractional integration of arbitrary order is introduced and applied together with spectral tau method for solving linear fractional differential equations (FDEs). The fractional integration is described in the Riemann-Liouville sense. The numerical approach is based on the shifted Chebyshev tau method. The main characteristic behind the approach using this technique is that only a small number of shifted Chebyshev polynomials is needed to obtain a satisfactory result. Illustrative examples reveal that the present method is very effective and convenient for linear multi-term FDEs. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：25 / 31

页数：7

共 20 条

[1]

[Anonymous], 2006, THEORY APPL FRACTION

[2] A quadrature tau method for fractional differential equations with variable coefficients [J].

Bhrawy, A. H. ;

Alofi, A. S. ;

Ezz-Eldien, S. S. .

APPLIED MATHEMATICS LETTERS, 2011, 24 (12) :2146-2152

[3]

Canuto C., 2012, Spectral Methods in Fluid Dynamics

[4]

Das S., 2008, Functional Fractional Calculus for System Identification and Controls

[5] Multi-order fractional differential equations and their numerical solution [J].

Diethelm, K ;

Ford, NJ .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 154 (03) :621-640

[6] Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials [J].

Doha, E. H. ;

Bhrawy, A. H. .

APPLIED NUMERICAL MATHEMATICS, 2008, 58 (08) :1224-1244

[7] A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order [J].

Doha, E. H. ;

Bhrawy, A. H. ;

Ezz-Eldien, S. S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (05) :2364-2373

[8] Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations [J].

Doha, E. H. ;

Bhrawy, A. H. ;

Ezz-Eldien, S. S. .

APPLIED MATHEMATICAL MODELLING, 2011, 35 (12) :5662-5672

[9] Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations [J].

Doha, E. H. ;

Bhrawy, A. H. ;

Saker, M. A. .

APPLIED MATHEMATICS LETTERS, 2011, 24 (04) :559-565

[10] A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations [J].

Esmaeili, Shahrokh ;

Shamsi, M. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (09) :3646-3654

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