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

Manel Amdouni, Jehad Alzabut, Mohammad Esmael Samei, Weerawat Sudsutad and Chatthai Thaiprayoon ()
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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
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

Mathematics, 2022, vol. 10, issue 19, 1-18

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.

Keywords: asymptotically; periodic functions; Gilpin–Ayala prey-predator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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