Spectral approximations to the fractional integral and derivative

Li, Changpin, Zeng, Fanhai, & Liu, Fawang (2012) Spectral approximations to the fractional integral and derivative. Fractional Calculus and Applied Analysis, 15(3), pp. 383-406.

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Abstract

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.

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ID Code: 60013
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: fractional integral, Caputo derivative, spectral approximation, Jacobi polynomials
DOI: 10.2478/s13540-012-0028-x
ISSN: 1314-2224 (online) 1311-0454 (print)
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Diogenes Co., Sofia
Copyright Statement: Author's Pre-print: author can archive pre-print (ie pre-refereeing)
Author's Post-print: author can archive post-print (ie final draft post-refereeing)
Publisher's Version/PDF: author cannot archive publisher's version/PDF
Deposited On: 15 May 2013 22:25
Last Modified: 20 May 2013 02:04

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