شاهرخ اسمعیلی

A family of nonstandard Gauss-Jacobi-Lobatto quadratures for numerical calculating integrals of the form $\int_{-1}^1 f'(x)(1-x)^\alpha{\D}x$‎, ‎$\alpha>-1$‎, ‎is derived and applied to approximation of the usual fractional derivative‎. ‎A software implementation of such quadratures was done by the recent {\sc Mathematica} package {\tt OrthogonalPolynomials} (cf‎. ‎[A.S.~Cvetkovi\'c‎, ‎G.V.~Milovanovi\'c‎, ‎Facta Univ‎. ‎Ser‎. ‎Math‎. ‎Inform‎. ‎{\bf19} (2004)‎, ‎17--36] and [G.V.~Milovanovi\'c‎, ‎A.S.~Cvetkovi\'c‎, ‎Math‎. ‎Balkanica {\bf26} (2012)‎, ‎169--184])‎. ‎Several numerical examples are presented and they show the effectiveness of the proposed approach‎.