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

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)...

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Veröffentlicht in:Applied mathematical modelling Jg. 37; H. 6; S. 4245 - 4252
Hauptverfasser: Bhrawy, A.H., Tharwat, M.M., Yildirim, A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.03.2013
Schlagworte:
Algorithms
Chebyshev approximation
Chebyshev–Gauss quadrature
Construction
Differential equations
Integrals
Mathematical models
Multi-term FDEs
Polynomials
Riemann–Liouville sense
Shifted Chebyshev polynomials
Spectra
Tau method
Chebyshev–Gauss quadrature
Tau method
Riemann–Liouville sense
Multi-term FDEs
Shifted Chebyshev polynomials
ISSN:0307-904X
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-2
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ISSN:0307-904X
DOI:10.1016/j.apm.2012.08.022