IJPAM: Volume 78, No. 8 (2012)

NUMERICAL STUDIES FOR
SOLVING FRACTIONAL-ORDER LOGISTIC EQUATION

N.H. Sweilam$^1$, M.M. Khader$^2$, A.M.S. Mahdy$^3$
$^1$Department of Mathematics
Faculty of Science
Cairo University
Giza, EGYPT
$^2$Department of Mathematics
Faculty of Science
Benha University
Benha, EGYPT
$^3$Department of Mathematics
Faculty of Science
Zagazig University
Zagazig, EGYPT


Abstract. In this paper, finite difference method (FDM) and variational iteration method (VIM) have been successfully implemented for solving non-linear fractional-order Logistic equation (FOLE). We have apply the concepts of fractional calculus to the well known population growth model in chaotic dynamic. The fractional derivative is described in the Caputo sense. The result is generalized of the classical population growth model to arbitrary order. The resulted non-linear system of algebraic equations using FDM is solved with the well know Newton iteration method. Where the condition of convergence is verified. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the proposed methods are extremely efficient to solve this complicated biological model.

Received: June 23, 2012

AMS Subject Classification: 65N06, 65N12, 65N15

Key Words and Phrases: fractional-order logistic equation, Caputo derivative, finite difference method, variational iteration method

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 8