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Modified fractional logistic equation

Author

Listed:
  • D’Ovidio, Mirko
  • Loreti, Paola
  • Sarv Ahrabi, Sima

Abstract

In the article (West, 2015), the author has obtained a function as the solution to fractional logistic equation (FLE). As demonstrated later in Area et al. (2016), this function (West function) is not the solution to FLE, but nevertheless as shown by West, it is in good agreement with the numerical solution to FLE. The West function indicates a compelling feature, in which the exponentials are substituted by Mittag-Leffler functions. In this paper, a modified fractional logistic equation (MFLE) is introduced, to which the West function is a solution. The proposed fractional integro-differential equation possesses a nonlinear additive term related to the solution of the logistic equation (LE). The method utilized in this article, may be applied to the analysis of solutions to nonlinear fractional differential equations of mathematical physics.

Suggested Citation

  • D’Ovidio, Mirko & Loreti, Paola & Sarv Ahrabi, Sima, 2018. "Modified fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 818-824.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:818-824
    DOI: 10.1016/j.physa.2018.04.011
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    References listed on IDEAS

    as
    1. Ortigueira, Manuel & Bengochea, Gabriel, 2017. "A new look at the fractionalization of the logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 554-561.
    2. West, Bruce J., 2015. "Exact solution to fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 103-108.
    3. Area, Iván & Losada, Jorge & Nieto, Juan J., 2016. "A note on the fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 182-187.
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    Cited by:

    1. Calatayud, Julia & Jornet, Marc & Mateu, Jorge & Pinto, Carla M.A., 2023. "A new population model for urban infestations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. D’Ovidio, Mirko & Loreti, Paola, 2018. "Solutions of fractional logistic equations by Euler’s numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1081-1092.
    3. Area, I. & Nieto, J.J., 2021. "Power series solution of the fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

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