Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators

: Khalighi Moein, Eftekhari Leila, Hosseinpour Soleiman, Lahti Leo

Publisher: MDPI

: 2021

: Symmetry

: SYMMETRY-BASEL

: ARTN 368

: 13

: 3

: 22

: 2073-8994

DOI: https://doi.org/10.3390/sym13030368

: https://research.utu.fi/converis/portal/detail/Publication/55080266

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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