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Title: A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives
Author: Jahanshahi, S.
Babolian, E.
Torres, D. F. M.
Vahidi, A. R.
Keywords: Fractional derivatives
Fractional differential equations
Fractional integrals
Fractional variational calculus
Gauss–Jacobi quadrature rule
Issue Date: 2017
Publisher: Elsevier
Abstract: We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving fractional boundary value problems. As an application, we solve a special class of fractional Euler–Lagrange equations. The method is based on Hale and Townsend algorithm for finding the roots and weights of the fractional Gauss–Jacobi quadrature rule and the predictor-corrector method introduced by Diethelm for solving fractional differential equations. Illustrative examples show that the given method is more accurate than the one introduced in [26], which uses the Golub–Welsch algorithm for evaluating fractional directional integrals. © 2017
Peer review: yes
DOI: 10.1016/j.chaos.2017.04.034
ISSN: 0960-0779
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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