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A fractal–fractional-order modified Predator–Prey mathematical model with immigrations

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  • Ali, Zeeshan
  • Rabiei, Faranak
  • Hosseini, Kamyar

Abstract

This manuscript aims to study a modified predator–prey model’s existence, stability, and dynamics under the newly developed fractal–fractional order operator in the Caputo–Fabrizio sense. The existence theory of the proposed model carries out through the Leray–Schauder alternative and sufficient conditions for stability are established using the classical technique of nonlinear functional analysis. The numerical results are obtained by the fractal–fractional Adam–Bashforth method in the Caputo–Fabrizio sense. The numerical results show that small immigrations invoke stable convergence in the predator–prey ecosystem. This means that a small number of sporadic immigrants can stabilize natural predator–prey populations.

Suggested Citation

  • Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.
    • Handle: RePEc:eee:matcom:v:207:y:2023:i:c:p:466-481
    DOI: 10.1016/j.matcom.2023.01.006
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    References listed on IDEAS

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    1. Zeeshan Ali & Shayan Naseri Nia & Faranak Rabiei & Kamal Shah & Ming Kwang Tan, 2021. "A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-13, July.
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    6. Zeeshan Ali & Poom Kumam & Kamal Shah & Akbar Zada, 2019. "Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations," Mathematics, MDPI, vol. 7(4), pages 1-26, April.
    7. Li, Zhongfei & Liu, Zhuang & Khan, Muhammad Altaf, 2020. "Fractional investigation of bank data with fractal-fractional Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    8. Mukhopadhyay, B. & Bhattacharyya, R., 2009. "Role of predator switching in an eco-epidemiological model with disease in the prey," Ecological Modelling, Elsevier, vol. 220(7), pages 931-939.
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    8. Mokni, Karima & Ch-Chaoui, Mohamed, 2024. "A Darwinian Beverton–Holt model with immigration effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 244-261.

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