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Article

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

1
Department of Computing, University of Turku, 20014 Turku, Finland
2
Department of Mathematics, Tarbiat Modares University, Tehran 1411713116, Iran
3
Department of Applied Mathematics, Shahrood University of Technology, Shahrood 3614773955, Iran
*
Author to whom correspondence should be addressed.
Academic Editor: Jan Awrejcewicz
Symmetry 2021, 13(3), 368; https://doi.org/10.3390/sym13030368
Received: 5 January 2021 / Revised: 21 January 2021 / Accepted: 26 January 2021 / Published: 25 February 2021
(This article belongs to the Section Mathematics and Symmetry/Asymmetry)
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. View Full-Text
Keywords: Caputo-Fabrizio operator; Lotka-Volterra differential equations; Adam-Bashforth method; stability analysis Caputo-Fabrizio operator; Lotka-Volterra differential equations; Adam-Bashforth method; stability analysis
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MDPI and ACS Style

Khalighi, M.; Eftekhari, L.; Hosseinpour, S.; Lahti, L. Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators. Symmetry 2021, 13, 368. https://doi.org/10.3390/sym13030368

AMA Style

Khalighi M, Eftekhari L, Hosseinpour S, Lahti L. Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators. Symmetry. 2021; 13(3):368. https://doi.org/10.3390/sym13030368

Chicago/Turabian Style

Khalighi, Moein, Leila Eftekhari, Soleiman Hosseinpour, and Leo Lahti. 2021. "Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators" Symmetry 13, no. 3: 368. https://doi.org/10.3390/sym13030368

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