A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations

被引：91
|
作者：
Bhrawy, A. H. [1 ,2 ]
Tharwat, M. M. [1 ,2 ]
Yildirim, A. [3 ]
机构：
[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia
[2] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf, Egypt
[3] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
来源：
APPLIED MATHEMATICAL MODELLING | 2013年 / 37卷 / 06期
关键词：
Multi-term FDEs; Tau method; Shifted Chebyshev polynomials; Chebyshev-Gauss quadrature; Riemann-Liouville sense; BOUNDARY-VALUE-PROBLEMS; OPERATIONAL MATRIX; WAVELET METHOD; COEFFICIENTS; COLLOCATION; EXPANSIONS; SYSTEMS;
D O I：
10.1016/j.apm.2012.08.022
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
A new explicit formula for the integrals of shifted Chebyshev polynomials of any degree for any fractional-order in terms of shifted Chebyshev polynomials themselves is derived. A fast and accurate algorithm is developed for the solution of linear multi-order fractional differential equations (FDEs) by considering their integrated forms. The shifted Chebyshev spectral tau (SCT) method based on the integrals of shifted Chebyshev polynomials is applied to construct the numerical solution for such problems. The method is then tested on examples. It is shown that the SCT yields better results. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：4245 / 4252
页数：8
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