International Journal of Differential Equations
Volume 2012 (2012), Article ID 845945, 8 pages
http://dx.doi.org/10.1155/2012/845945
Research Article

Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model

Najeeb Alam Khan,1 Amir Mahmood,2 Nadeem Alam Khan,1 and Asmat Ara1

1Department of Mathematical Sciences, University of Karachi, Karachi 75270, Pakistan
2Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan

Received 30 May 2012; Accepted 17 October 2012

Academic Editor: Wen Chen

Copyright © 2012 Najeeb Alam Khan 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

This paper suggests two component homotopy method to solve nonlinear fractional integrodifferential equations, namely, Volterra's population model. Padé approximation was effectively used in this method to capture the essential behavior of solutions for the mathematical model of accumulated effect of toxins on a population living in a closed system. The behavior of the solutions and the effects of different values of fractional-order are indicated graphically. The study outlines significant features of this method as well as sheds some light on advantages of the method over the other. The results show that this method is very efficient, convenient, and can be adapted to fit a larger class of problems.