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Mathematical Problems in Engineering
Volume 2013, Article ID 391901, 7 pages
http://dx.doi.org/10.1155/2013/391901
Research Article

On Approximate Solutions for Fractional Logistic Differential Equation

1Department of Mathematics and Statistics, College of Science, Al-Imam Mohammed Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia
2Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

Received 6 March 2013; Revised 1 April 2013; Accepted 2 April 2013

Academic Editor: Guo-Cheng Wu

Copyright © 2013 M. M. Khader and Mohammed M. Babatin. 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 approximate formula of the fractional derivatives is derived. The proposed formula is based on the generalized Laguerre polynomials. Global approximations to functions defined on a semi-infinite interval are constructed. The fractional derivatives are presented in terms of Caputo sense. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. The new spectral Laguerre collocation method is presented for solving fractional Logistic differential equation (FLDE). The properties of Laguerre polynomials approximation are used to reduce FLDE to solve a system of algebraic equations which is solved using a suitable numerical method. Numerical results are provided to confirm the theoretical results and the efficiency of the proposed method.