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Dynamical Analysis of Nutrient-Phytoplankton-Zooplankton Model with Viral Disease in Phytoplankton Species under Atangana-Baleanu-Caputo Derivative

Author

Listed:
  • Songkran Pleumpreedaporn

    (Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
    These authors contributed equally to this work.)

  • Chanidaporn Pleumpreedaporn

    (Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
    These authors contributed equally to this work.)

  • Jutarat Kongson

    (Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    Center of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
    These authors contributed equally to this work.)

  • Chatthai Thaiprayoon

    (Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    Center of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
    These authors contributed equally to this work.)

  • Jehad Alzabut

    (Deparment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey
    These authors contributed equally to this work.)

  • Weerawat Sudsutad

    (Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
    These authors contributed equally to this work.)

Abstract

A mathematical model of the nutrient-phytoplankton-zooplankton associated with viral infection in phytoplankton under the Atangana-Baleanu derivative in Caputo sense is investigated in this study. We prove the theoretical results for the existence and uniqueness of the solutions by using Banach’s and Sadovskii’s fixed point theorems. The notion of various Ulam’s stability is used to guarantee the context of the stability analysis. Furthermore, the equilibrium points and the basic reproduction numbers for the proposed model are provided. The Adams type predictor-corrector algorithm has been applied for the theoretical confirmation to establish the approximate solutions. A variety of numerical plots corresponding to various fractional orders between zero and one are presented to describe the dynamical behavior of the fractional model under consideration.

Suggested Citation

  • Songkran Pleumpreedaporn & Chanidaporn Pleumpreedaporn & Jutarat Kongson & Chatthai Thaiprayoon & Jehad Alzabut & Weerawat Sudsutad, 2022. "Dynamical Analysis of Nutrient-Phytoplankton-Zooplankton Model with Viral Disease in Phytoplankton Species under Atangana-Baleanu-Caputo Derivative," Mathematics, MDPI, vol. 10(9), pages 1-33, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1578-:d:810338
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    References listed on IDEAS

    as
    1. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    2. Ghanbari, Behzad & Gómez-Aguilar, J.F., 2018. "Modeling the dynamics of nutrient–phytoplankton–zooplankton system with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 114-120.
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    Cited by:

    1. Marisa Kaewsuwan & Rachanee Phuwapathanapun & Weerawat Sudsutad & Jehad Alzabut & Chatthai Thaiprayoon & Jutarat Kongson, 2022. "Nonlocal Impulsive Fractional Integral Boundary Value Problem for ( ρ k , ϕ k )-Hilfer Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 10(20), pages 1-40, October.
    2. Asamoah, Joshua Kiddy K. & Fatmawati,, 2023. "A fractional mathematical model of heartwater transmission dynamics considering nymph and adult amblyomma ticks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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