ANALYSIS OF TRITROPHIC INTERACTION WITH VOLATILE COMPOUNDS IN PLANTS WITH FRACTAL–FRACTIONAL CAPUTO OPERATOR

Tariq Mahmood, Fuad S. Al-Duais, Adnan Sami and Mei Sun
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Tariq Mahmood: School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013 Jiangsu, P. R. China
Fuad S. Al-Duais: ��Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam bin Abdulaziz University, Al-Aflaj 11942, Saudi Arabia‡Administration Department, Administrative Science College, Thamar University, Thamar, Yemen
Adnan Sami: �Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhwa, Pakistan
Mei Sun: School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013 Jiangsu, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-13

Abstract: This paper is devoted to the study of the dynamical behavior of the tritrophic interaction amongst plants, herbivores and carnivores mathematical model, expressed by three nonlinear ordinary differential equations under fractal–fractional derivative in the Caputo sense. We use fixed point theory to ensure that one solution exists to the proposed model. In addition, Hyers–Ulam’s stability analysis is studied by using theorem of functional analysis. For the numerical solution, we apply the fractional Adams–Bashforth iterative technique. For arbitrary fractional order and fractal dimensions, we study the dynamical and chaotic behavior of the obtained results for the considered model. Using Matlab 16, the system is then solved to get the required numerical solution for the proposed system. From the numerical simulations, we observed that the decay in fractional order dynamics of the system is stabilized when the amplitude of the oscillations becomes smaller.

Keywords: Plants Tritrophic Interaction; Chaotic Theory; Fractal–Fractional Caputo; Existence Results; Ulam–Hyers Stability; Numerical Simulations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400820

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