Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann-Liouville integrals

摘要

Inspired with papers by Bokhari, Qadir, and Al-Attas (2010) and by Rapaic, Sekara, and Govedarica (2014), in this paper we investigate a few types of orthogonal polynomials on finite intervals and derive the corresponding quadrature formulas of Gaussian type for efficient numerical computation of the left and right fractional Riemann-Liouville integrals. Several numerical examples are included to demonstrate the numerical efficiency of the proposed procedure.