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BY-NC-ND 3.0 license Open Access Published by De Gruyter September 3, 2014

Nonstandard Gauss—Lobatto quadrature approximation to fractional derivatives

Shahrokh Esmaeili and Gradimir Milovanović

Abstract

A family of nonstandard Gauss-Jacobi-Lobatto quadratures for numerical calculating integrals of the form ∫-11 f′(x)(1-x)α dx, α > -1, is derived and applied to approximation of the usual fractional derivative. A software implementation of such quadratures was done by the recent Mathematica package OrthogonalPolynomials (cf. [A.S. Cvetković, G.V. Milovanović, Facta Univ. Ser. Math. Inform. 19 (2004), 17–36] and [G.V. Milovanović, A.S. Cvetković, Math. Balkanica 26 (2012), 169–184]). Several numerical examples are presented and they show the effectiveness of the proposed approach.

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Published Online: 2014-9-3
Published in Print: 2014-12-1

© 2014 Diogenes Co., Sofia

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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