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
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Open Access publication channel
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/55080266
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
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.
Keywords:
Adam-Bashforth method, Caputo-Fabrizio operator, Lotka-Volterra differential equations, stability analysis
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