IJPAM: Volume 78, No. 8 (2012)
SOLVING FRACTIONAL-ORDER LOGISTIC EQUATION




Faculty of Science
Cairo University
Giza, EGYPT

Faculty of Science
Benha University
Benha, EGYPT

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
Download paper from here.
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