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.
Administrators only | Request a copy from author
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.
Impact and interest:
Citation counts are sourced monthly from and citation databases.
These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.
Citations counts from theindexing service can be viewed at the linked Google Scholar™ search.
|Item Type:||Journal Article|
|Keywords:||fractional integral, Caputo derivative, spectral approximation, Jacobi polynomials|
|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|
Repository Staff Only: item control page