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Fractional logistic models in the frame of fractional operators generated by conformable derivatives

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  • Abdeljawad, Thabet
  • Al-Mdallal, Qasem M.
  • Jarad, Fahd

Abstract

In this article, we study different types of fractional-order logistic models in the frame of Caputo type fractional operators generated by conformable derivatives (Caputo CFDs). We present the existence and uniqueness theorems to solutions of these models and discuss their stability by perturbing the equilibrium points. Finally, we furniture our results by illustrative numerical examples for the studied models.

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  • Abdeljawad, Thabet & Al-Mdallal, Qasem M. & Jarad, Fahd, 2019. "Fractional logistic models in the frame of fractional operators generated by conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 94-101.
    • Handle: RePEc:eee:chsofr:v:119:y:2019:i:c:p:94-101
    DOI: 10.1016/j.chaos.2018.12.015
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    1. Zhao, Dazhi & Pan, Xueqin & Luo, Maokang, 2018. "A new framework for multivariate general conformable fractional calculus and potential applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 271-280.
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    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.
    4. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    5. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
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    Cited by:

    1. Khan, Aziz & Khan, Hasib & Gómez-Aguilar, J.F. & Abdeljawad, Thabet, 2019. "Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 422-427.
    2. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
    3. Abdullahi, Auwal, 2021. "Modelling of transmission and control of Lassa fever via Caputo fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. BİLDİK, Necdet & DENİZ, Sinan & SAAD, Khaled M., 2020. "A comparative study on solving fractional cubic isothermal auto-catalytic chemical system via new efficient technique," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    5. Khan, Hasib & Khan, Aziz & Jarad, Fahd & Shah, Anwar, 2020. "Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Fall, Aliou Niang & Ndiaye, Seydou Nourou & Sene, Ndolane, 2019. "Black–Scholes option pricing equations described by the Caputo generalized fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 108-118.
    7. Fernando Alcántara-López & Carlos Fuentes & Carlos Chávez & Fernando Brambila-Paz & Antonio Quevedo, 2021. "Fractional Growth Model Applied to COVID-19 Data," Mathematics, MDPI, vol. 9(16), pages 1-13, August.
    8. Acay, Bahar & Bas, Erdal & Abdeljawad, Thabet, 2020. "Fractional economic models based on market equilibrium in the frame of different type kernels," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    9. Fernando Alcántara-López & Carlos Fuentes & Carlos Chávez & Jesús López-Estrada & Fernando Brambila-Paz, 2022. "Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data," Mathematics, MDPI, vol. 10(5), pages 1-18, March.
    10. Begum, Razia & Tunç, Osman & Khan, Hasib & Gulzar, Haseena & Khan, Aziz, 2021. "A fractional order Zika virus model with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    11. Khan, Aziz & Abdeljawad, Thabet & Gómez-Aguilar, J.F. & Khan, Hasib, 2020. "Dynamical study of fractional order mutualism parasitism food web module," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    12. Ávalos-Ruiz, L.F. & Gómez-Aguilar, J.F. & Atangana, A. & Owolabi, Kolade M., 2019. "On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 364-388.
    13. Xie, Wanli & Liu, Caixia & Wu, Wen-Ze & Li, Weidong & Liu, Chong, 2020. "Continuous grey model with conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    14. Baogui Xin & Wei Peng & Yekyung Kwon & Yanqin Liu, 2019. "Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk," Papers 1903.12267, arXiv.org, revised Apr 2019.

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