{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T02:19:44Z","timestamp":1774491584465,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,2,25]],"date-time":"2021-02-25T00:00:00Z","timestamp":1614211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["295741"],"award-info":[{"award-number":["295741"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym13030368","type":"journal-article","created":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T06:47:20Z","timestamp":1614322040000},"page":"368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8176-0367","authenticated-orcid":false,"given":"Moein","family":"Khalighi","sequence":"first","affiliation":[{"name":"Department of Computing, University of Turku, 20014 Turku, Finland"}]},{"given":"Leila","family":"Eftekhari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tarbiat Modares University, Tehran 1411713116, Iran"}]},{"given":"Soleiman","family":"Hosseinpour","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Shahrood University of Technology, Shahrood 3614773955, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5537-637X","authenticated-orcid":false,"given":"Leo","family":"Lahti","sequence":"additional","affiliation":[{"name":"Department of Computing, University of Turku, 20014 Turku, Finland"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.cnsns.2018.04.019","article-title":"A new collection of real world applications of fractional calculus in science and engineering","volume":"64","author":"Sun","year":"2018","journal-title":"Commun. 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