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On Nonlinear Fractional-Order Mathematical Model Of Food-Chain

Author

Listed:
  • KOTTAKKARAN SOOPPY NISAR

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia)

  • MATI UR RAHMAN

    (Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, P. R. China)

  • GHAYLEN LAOUINI

    (College of Engineering and Technology, American University of the Middle East, Kuwait)

  • MESHAL SHUTAYWI

    (Department of Mathematics, College of Science & Arts, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia)

  • MUHAMMAD ARFAN

    (Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000 Khyber Pakhtunkhwa, Pakistan)

Abstract

This paper investigates the dynamical semi-analysis of the delayed food chain model under the considered fractional order. The food chain model is composed of three compartments, namely, population of the prey, intermediate predator and a top predator. By using the fixed point theorem approach, we exploit some conditions for existence results and stability for the considered system via Atangana–Baleanu–Caputo derivative with fractional order. Also, using the well-known Adam–Bashforth technique for numerics, we simulate the concerning results for the interference between the prey and intermediate predator. Graphical results are discussed for different fractional-order values for the considered model.

Suggested Citation

  • Kottakkaran Sooppy Nisar & Mati Ur Rahman & Ghaylen Laouini & Meshal Shutaywi & Muhammad Arfan, 2022. "On Nonlinear Fractional-Order Mathematical Model Of Food-Chain," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-12, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x2240014x
    DOI: 10.1142/S0218348X2240014X
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