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Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays
Faculty
Science
Year:
2012
Type of Publication:
Article
Pages:
Authors:
Khader, M. M, Sweilam, N. H, Mahdy, A. M. S
DOI:
10.1155/2012/764894
Journal:
JOURNAL OF APPLIED MATHEMATICS HINDAWI PUBLISHING CORPORATION
Volume:
Research Area:
Mathematics
ISSN
ISI:000309285800001
Keywords :
Numerical Studies , Fractional-Order Logistic Differential Equation
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.
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