A1 Refereed original research article in a scientific journal
Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators
Authors: Khalighi Moein, Eftekhari Leila, Hosseinpour Soleiman, Lahti Leo
Publisher: MDPI
Publication year: 2021
Journal: Symmetry
Journal name in source: SYMMETRY-BASEL
Journal acronym: SYMMETRY-BASEL
Article number: ARTN 368
Volume: 13
Issue: 3
Number of pages: 22
eISSN: 2073-8994
DOI: https://doi.org/10.3390/sym13030368
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/55080266
Abstract
In this paper, we apply the concept of fractional calculus to study three-dimensional Lotka-Volterra differential equations. We incorporate the Caputo-Fabrizio fractional derivative into this model and investigate the existence of a solution. We discuss the uniqueness of the solution and determine under what conditions the model offers a unique solution. We prove the stability of the nonlinear model and analyse the properties, considering the non-singular kernel of the Caputo-Fabrizio operator. We compare the stability conditions of this system with respect to the Caputo-Fabrizio operator and the Caputo fractional derivative. In addition, we derive a new numerical method based on the Adams-Bashforth scheme. We show that the type of differential operators and the value of orders significantly influence the stability of the Lotka-Volterra system and numerical results demonstrate that different fractional operator derivatives of the nonlinear population model lead to different dynamical behaviors.
In this paper, we apply the concept of fractional calculus to study three-dimensional Lotka-Volterra differential equations. We incorporate the Caputo-Fabrizio fractional derivative into this model and investigate the existence of a solution. We discuss the uniqueness of the solution and determine under what conditions the model offers a unique solution. We prove the stability of the nonlinear model and analyse the properties, considering the non-singular kernel of the Caputo-Fabrizio operator. We compare the stability conditions of this system with respect to the Caputo-Fabrizio operator and the Caputo fractional derivative. In addition, we derive a new numerical method based on the Adams-Bashforth scheme. We show that the type of differential operators and the value of orders significantly influence the stability of the Lotka-Volterra system and numerical results demonstrate that different fractional operator derivatives of the nonlinear population model lead to different dynamical behaviors.
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