A Note on a Fractional Extension of the Lotka–Volterra Model Using the Rabotnov Exponential Kernel-Reference-Cited by-同舟云学术

A Note on a Fractional Extension of the Lotka–Volterra Model Using the Rabotnov Exponential Kernel

Published:2024-01-21 Issue:1 Volume:13 Page:71
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Khader Mohamed M.¹²^ORCID,Macías-Díaz Jorge E.³⁴^ORCID,Román-Loera Alejandro⁵^ORCID,Saad Khaled M.⁶⁷^ORCID

Affiliation:

1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia

2. Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt

3. Department of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia

4. Department of Mathematics and Physics, Autonomous University of Aguascalientes, Ave. Universidad 940, Ciudad Universitaria, Aguascalientes 20100, Mexico

5. Department of Electronics, Autonomous University of Aguascalientes, Ave. Universidad 940, Ciudad Universitaria, Aguascalientes 20100, Mexico

6. Department of Mathematics, College of Sciences and Arts, Najran University, Najran P.O. Box 1988, Saudi Arabia

7. Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz P.O. Box 6803, Yemen

Abstract

In this article, we study the fractional form of a well-known dynamical system from mathematical biology, namely, the Lotka–Volterra model. This mathematical model describes the dynamics of a predator and prey, and we consider here the fractional form using the Rabotnov fractional-exponential (RFE) kernel. In this work, we derive an approximate formula of the fractional derivative of a power function ζp in terms of the RFE kernel. Next, by using the spectral collocation method (SCM) based on the shifted Vieta–Lucas polynomials (VLPs), the fractional differential system is reduced to a set of algebraic equations. We provide a theoretical convergence analysis for the numerical approach, and the accuracy is verified by evaluating the residual error function through some concrete examples. The results are then contrasted with those derived using the fourth-order Runge-Kutta (RK4) method.

Funder

National Council of Science and Technology of Mexico

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/13/1/71/pdf

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