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Mathematical Problems in Engineering
Volume 2013, Article ID 161030, 8 pages
http://dx.doi.org/10.1155/2013/161030
Research Article

Legendre Wavelets Method for Solving Fractional Population Growth Model in a Closed System

1Faculty of Mathematics, Yazd University, Yazd 89195741, Iran
2Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy
3School of Information Science & Technology, East China Normal University, Shanghai 200241, China

Received 7 August 2013; Accepted 17 August 2013

Academic Editor: Cristian Toma

Copyright © 2013 M. H. Heydari 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 order integration for Legendre wavelets is derived. Block pulse functions and collocation method are employed to derive a general procedure for forming this matrix. Moreover, a computational method based on wavelet expansion together with this operational matrix is proposed to obtain approximate solution of the fractional population growth model of a species within a closed system. The main characteristic of the new approach is to convert the problem under study to a nonlinear algebraic equation.