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Analysis Of Tritrophic Interaction With Volatile Compounds In Plants With Fractal–Fractional Caputo Operator

Author

Listed:
  • 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)

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.

Suggested Citation

  • Tariq Mahmood & Fuad S. Al-Duais & Adnan Sami & Mei Sun, 2023. "Analysis Of Tritrophic Interaction With Volatile Compounds In Plants With Fractal–Fractional Caputo Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x23400820
    DOI: 10.1142/S0218348X23400820
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