Nonstandard Gauss-Lobatto quadrature approximation to fractional derivatives

作者：Esmaeili Shahrokh^*; Milovanovic Gradimir V

来源：Fractional Calculus and Applied Analysis, 2014, 17(4): 1075-1099.

DOI：10.2478/s13540-014-0215-z

• fractional derivative
• quadrature rule
• Gaussian quadrature
• nodes
• weights
• software implementation
• MATHEMATICA package

A family of nonstandard Gauss-Jacobi-Lobatto quadratures for numerical calculating integrals of the form integral(1)(-1) f'(x)(1-x)(alpha) dx, alpha > -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. Cvetkovic, G.V. Milovanovic, Facta Univ. Ser. Math. Inform. 19 (2004), 17-36] and [G.V. Milovanovic, A.S. Cvetkovic, Math. Balkanica 26 (2012), 169-184]). Several numerical examples are presented and they show the effectiveness of the proposed approach.

• 出版日期2014-12