ON NONLINEAR FRACTIONAL-ORDER MATHEMATICAL MODEL OF FOOD-CHAIN

Kottakkaran Sooppy Nisar, Mati Ur Rahman, Ghaylen Laouini (), Meshal Shutaywi () and Muhammad Arfan ()
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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

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-12

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.

Keywords: Food-Chain Model; Existence Result; ABC Derivative; Adams–Bashforth Method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X2240014X

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