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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 546502, 10 pages
Research Article

Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems

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, Saudi Arabia
3Institute of Space Sciences, Magurele-Bucharest, Romania
4Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
5Department of Mathematics, Faculty of Science, Beni-Suef University, Beni Suef, Egypt

Received 15 April 2013; Accepted 21 May 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.


We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs) on semi-infinite interval, using generalized Laguerre polynomials. We derive the operational matrix of Caputo fractional derivative of the generalized Laguerre polynomials which is applied together with generalized Laguerre tau approximation for implementing a spectral solution of linear multiterm FDEs on semi-infinite interval subject to initial conditions. The generalized Laguerre pseudo-spectral approximation based on the generalized Laguerre operational matrix is investigated to reduce the nonlinear multiterm FDEs and its initial conditions to nonlinear algebraic system, thus greatly simplifying the problem. Through several numerical examples, we confirm the accuracy and performance of the proposed spectral algorithms. Indeed, the methods yield accurate results, and the exact solutions are achieved for some tested problems.