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Power series solution of the fractional logistic equation

Author

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  • Area, I.
  • Nieto, J.J.

Abstract

Using a series of fractional powers we present a representation of the solution to the fractional logistic equation is presented. To simplify we consider the simplest case and prove that the power series is indeed the exact solution. Some numerical approximations are presented to show the good approximations obtained by truncating the fractional power series.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:573:y:2021:i:c:s0378437121002193
    DOI: 10.1016/j.physa.2021.125947
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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. 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.
    3. Tarasova, Valentina V. & Tarasov, Vasily E., 2017. "Logistic map with memory from economic model," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 84-91.
    4. West, Bruce J., 2015. "Exact solution to fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 103-108.
    5. 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.
    6. Pelinovsky, Efim & Kurkin, Andrey & Kurkina, Oxana & Kokoulina, Maria & Epifanova, Anastasia, 2020. "Logistic equation and COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. 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.
    8. Nosrati, Komeil & Shafiee, Masoud, 2018. "Fractional-order singular logistic map: Stability, bifurcation and chaos analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 224-238.
    9. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
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    Cited by:

    1. Simon, S. Gimnitz & Bira, B. & Zeidan, Dia, 2023. "Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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