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

Numerical studies for fractional-order logistic differential equation with two different delays. (English) Zbl 1251.65118

J. Appl. Math. 2012, Article ID 764894, 14 p. (2012).
Summary: 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 the 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.

Cited in 33 Documents

MSC:

65L99 Numerical methods for ordinary differential equations
34A08 Fractional ordinary differential equations

Keywords:

fractional-order logistic differential equation; Chebyshev approximations
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References:

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