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A Generalized Approach of the Gilpin–Ayala Model with Fractional Derivatives under Numerical Simulation

Author

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  • Manel Amdouni

    (Laboratory of Mathematical Physic, Specials Functions and Applications, LR11ES35, Ecole Supérieure des Sciences et de Technologie de Hammam-Sousse, Université de Sousse, Sousse 4054, Tunisia)

  • Jehad Alzabut

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Türkiye)

  • Mohammad Esmael Samei

    (Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan 65178, Iran)

  • Weerawat Sudsutad

    (Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand)

  • Chatthai Thaiprayoon

    (Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand)

Abstract

In this article, we study the existence and uniqueness of multiple positive periodic solutions for a Gilpin–Ayala predator-prey model under consideration by applying asymptotically periodic functions. The result of this paper is completely new. By using Comparison Theorem and some technical analysis, we showed that the classical nonlinear fractional model is bounded. The Banach contraction mapping principle was used to prove that the model has a unique positive asymptotical periodic solution. We provide an example and numerical simulation to inspect the correctness and availability of our essential outcomes.

Suggested Citation

  • Manel Amdouni & Jehad Alzabut & Mohammad Esmael Samei & Weerawat Sudsutad & Chatthai Thaiprayoon, 2022. "A Generalized Approach of the Gilpin–Ayala Model with Fractional Derivatives under Numerical Simulation," Mathematics, MDPI, vol. 10(19), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3655-:d:934334
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    References listed on IDEAS

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    1. Yongzhi Liao & Yongkun Li & Xiaoyan Dou, 2012. "Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harvesting Terms," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, June.
    2. Amdouni, Manel & Chérif, Farouk, 2018. "The pseudo almost periodic solutions of the new class of Lotka–Volterra recurrent neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 79-88.
    3. Shuo Zhang & Yongguang Yu & Wei Hu, 2014. "Robust Stability Analysis of Fractional-Order Hopfield Neural Networks with Parameter Uncertainties," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-14, April.
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    Cited by:

    1. Baishya, Chandrali & Premakumari, R.N. & Samei, Mohammad Esmael & Naik, Manisha Krishna, 2023. "Chaos control of fractional order nonlinear Bloch equation by utilizing sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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