A Generalized Approach of the Gilpin–Ayala Model with Fractional Derivatives under Numerical Simulation
Manel Amdouni,
Jehad Alzabut,
Mohammad Esmael Samei,
Weerawat Sudsutad,
Chatthai Thaiprayoon
Affiliations
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
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.
