Journal of Applied Mathematics

Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays

N. H. Sweilam, M. M. Khader, and A. M. S. Mahdy

Full-text: Open access

Abstract

A numerical method for solving the fractional-order logistic differential equation with two different delays (FOLE) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce FOLE to a system of algebraic equations. Special attention is given to study the convergence and the error estimate of the presented method. Numerical illustrations are presented to demonstrate utility of the proposed method. Chaotic behavior is observed and the smallest fractional order for the chaotic behavior is obtained. Also, FOLE is studied using variational iteration method (VIM) and the fractional complex transform is introduced to convert fractional Logistic equation to its differential partner, so that its variational iteration algorithm can be simply constructed. Numerical experiment is presented to illustrate the validity and the great potential of both proposed techniques.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 764894, 14 pages.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153499

Digital Object Identifier
doi:10.1155/2012/764894

Mathematical Reviews number (MathSciNet)
MR2970445

Zentralblatt MATH identifier
1251.65118

Citation

Sweilam, N. H.; Khader, M. M.; Mahdy, A. M. S. Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays. J. Appl. Math. 2012 (2012), Article ID 764894, 14 pages. doi:10.1155/2012/764894. https://projecteuclid.org/euclid.jam/1357153499


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