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Abstract and Applied Analysis
Volume 2013, Article ID 413529, 12 pages
Research Article

A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

1Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29.Km, 06810 Ankara, Turkey
2Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Institute of Space Sciences, Magurele-Bucharest, Romania
4Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
5Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt

Received 21 May 2013; Accepted 7 July 2013

Academic Editor: Soheil Salahshour

Copyright © 2013 D. Baleanu 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.


This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method. The spatial approximation with its Caputo fractional derivatives is based on modified generalized Laguerre polynomials with , , and , and is the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.