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Dynamical study of fractional order mutualism parasitism food web module

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  • Khan, Aziz
  • Abdeljawad, Thabet
  • Gómez-Aguilar, J.F.
  • Khan, Hasib

Abstract

In literature, many researchers have examined food web modules for different aspects and kinds such as exploitative competition, energy flow web, apparent competition, source web, trophic cascades of food chains, functional web, paleoecological web and intraguild predation. These food webs have been analyzed for competition and predation, where as the module connected with mutualism and parasitism have attracted the attention of researchers. In this article, we study mutualism parasitism food web module (MPFWM) by replacing the ordinary derivative by Atangana-Baleanu (AB) fractional order (FO) derivative, which is a generalization of classical derivative. This new type of operators enables us to use the essential information of the variables in the nonlocal systems. Existence and uniqueness (EU) of solutions have been proved by employing fixed point theorem. Picard’s stability approach is used for the stability analysis. Finally, numerical solutions of the ABC fractional order MPFWM were obtained for the particular parameter values.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920300874
    DOI: 10.1016/j.chaos.2020.109685
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    Cited by:

    1. Li, Xiaoyan, 2021. "Comment for “Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel”," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Partohaghighi, Mohammad & Akgül, Ali, 2021. "Modelling and simulations of the SEIR and Blood Coagulation systems using Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. 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).
    4. Ajay Kumar & Sara Salem Alzaid & Badr Saad T. Alkahtani & Sunil Kumar, 2022. "Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    5. Tariq Q. S. Abdullah & Gang Huang & Wadhah Al-Sadi & Yasser Aboelmagd & Wael Mobarak, 2024. "Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme," Mathematics, MDPI, vol. 12(15), pages 1-24, July.
    6. Singh, Harendra & Baleanu, Dumitru & Singh, Jagdev & Dutta, Hemen, 2021. "Computational study of fractional order smoking model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Mashayekhi, S. & Sedaghat, S., 2021. "Fractional model of stem cell population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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