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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 569286, 7 pages
http://dx.doi.org/10.1155/2013/569286
Research Article

On a Generalized Laguerre Operational Matrix of Fractional Integration

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
3Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29.km, 06810 Yenimahalle Ankara, Turkey
4Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
5Institute of Space Sciences, RO 76900, Magurele-Bucharest, Romania
6Department of Mathematics, Faculty of Science, Umm Al-Qura University, Mecca 21955, Saudi Arabia
7Department of Electrical Engineering, Polytechnic of Porto, Institute of Engineering, 4314200-072 Porto, Portugal

Received 18 December 2012; Accepted 18 January 2013

Academic Editor: József Kázmér Tar

Copyright © 2013 A. H. Bhrawy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new operational matrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived. The fractional integration is described in the Riemann-Liouville sense. This operational matrix is applied together with generalized Laguerre tau method for solving general linear multiterm fractional differential equations (FDEs). The method has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposed method is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.