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Some Orthogonal Polynomials on the Finite Interval and Gaussian Quadrature Rules for Fractional Riemann-Liouville Integrals
  • Gradimir Milovanovic
Gradimir Milovanovic
Serbian Academy of Sciences and Arts
Author Profile

Peer review status:Published

13 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
19 Jun 2020Submission Checks Completed
19 Jun 2020Assigned to Editor
19 Jun 2020Reviewer(s) Assigned
27 Jun 2020Review(s) Completed, Editorial Evaluation Pending
28 Jun 2020Editorial Decision: Revise Minor
11 Jul 20201st Revision Received
12 Jul 2020Submission Checks Completed
12 Jul 2020Assigned to Editor
12 Jul 2020Editorial Decision: Accept
30 Jul 2020Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.6752

Abstract

Inspired by papers by M.A. Bokhari, A. Qadir, and H. Al-Attas [On Gauss-type quadrature rules, Numer. Funct. Anal. Optim. 31 (2010), 1120-1134] and by M.R. Rapaic, T.B. Sekara, and V. Govedarica [A novel class of fractionally orthogonal quasi-polynomials and new fractional quadrature formulas, Appl. Math. Comput. 245 (2014), 206-219], 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.