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

Author

Listed:
  • N. H. Sweilam
  • M. M. Khader
  • A. M. S. Mahdy

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.

Suggested Citation

  • N. H. Sweilam & M. M. Khader & A. M. S. Mahdy, 2012. "Numerical Studies for Fractional‐Order Logistic Differential Equation with Two Different Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:764894
    DOI: 10.1155/2012/764894
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    References listed on IDEAS

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    1. Sweilam, N.H. & Khader, M.M., 2007. "Variational iteration method for one dimensional nonlinear thermoelasticity," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 145-149.
    2. Davis, L.C., 2003. "Modifications of the optimal velocity traffic model to include delay due to driver reaction time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 557-567.
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