ON SOME FRACTIONAL MODELS OF LOTKA-VOLTERRA
Keywords:
fractional derivative in Caputo’s sense, fractional integral, prey-predation, Adomian method, Lotka-VolterraDOI:
https://doi.org/10.17654/0975045225009Abstract
In this paper, we study two fractional models of Lotka-Volterra.
We begin by recalling the fundamental notions of fractional analysis. Then we proceed in a second step to give the description of the Adomian method and we finish our work with the description and resolution of some fractional models of Lotka-Volterra. In the first two models, we introduce diffusion terms. In the third, we try to model a food chain with three populations, by putting two species in competition for food (rabbits and sheep), and by introducing a predatory species (wolves).
Received: September 28, 2024
Accepted: November 27, 2024
References
Bamogo Hamadoun, Francis Bassono and Traoré André, Numerical resolution of the biological population model by the SBA method, Universal Journal of Mathematics and Mathematical Sciences 19(2) (2023), 119-137.
http://dx.doi.org/10.17654/2277141723020.
Brahim Tellab, Thèse: Résolution des équations différentielles fractionnaires, Université des Frères Mentouri Constantine-1, 2018.
Francis BASSONO, Résolution numérique comparé de quelques equations fonctionnelles par les méthodes Somé Blaise Abbo (SBA), décompositionnelle d’Adomian et perturbation, Thèse de doctorat unique, Université Ouaga I Pr. Joseph KI-ZERBO, UFR/SEA, LANIBIO, Burkina Faso, 2013.
François Dubois, Ana Cristina Galucio and Nelly Point, Introduction à la derivation fractionnaire, Théorie et Applications, 2010.
francois.dubois@math.u-psud.fr, anacristina.galucio@eads.net,
nelly.point@cnam.fr.
https://fr.wikipedia.org/wiki/Analyse_fractionnaire#:~:text=L’analyse%20 fractionnaire%20est%20une,g%C3%A9n%C3%A9ral%20des%20op%C3%A9rateurs%20pseudo%2Ddiff%C3%A9rentiels.
Manon de la Tousche, Autour des équations de Lotka-Volterra et quelques apparentées en biologie : EDO, EDP, simulations, Sorbonne Université, 2022.
Youssouf Paré, Équations intégrales et intégro-différentielles, Generis Publishing, www.generis-publishing.com, Copyright 2021.
Youssouf Paré, Résolution de quelques équations fonctionnelles par la méthode numérique SBA (SOME BLAISE-ABBO), Thèse de Doctorat unique, Université de Ouagadougou, UFR SEA, Département de Mathématiques et Informatique, Burkina Faso, 2010.
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