{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T12:16:57Z","timestamp":1788783417192,"version":"build-2803163510"},"reference-count":50,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,20]],"date-time":"2018-05-20T00:00:00Z","timestamp":1526774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich\u2013Fabrikant, Thomas\u2019 cyclically symmetric attractor and Newton\u2013Leipnik. Fractional conformable and   \u03b2   -conformable derivatives of Liouville\u2013Caputo type are considered to solve the proposed systems. A numerical method based on the Adams\u2013Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and   \u03b2   -conformable attractors are provided to illustrate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/e20050384","type":"journal-article","created":{"date-parts":[[2018,5,21]],"date-time":"2018-05-21T04:07:30Z","timestamp":1526875650000},"page":"384","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["Chaotic Attractors with Fractional Conformable Derivatives in the Liouville\u2013Caputo Sense and Its Dynamical Behaviors"],"prefix":"10.3390","volume":"20","author":[{"given":"Jes\u00fas Emmanuel Sol\u00eds","family":"P\u00e9rez","sequence":"first","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Interior Internado Palmira S\/N, Col. Palmira, C.P. 62490 Cuernavaca, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9403-3767","authenticated-orcid":false,"given":"Jos\u00e9 Francisco","family":"G\u00f3mez-Aguilar","sequence":"additional","affiliation":[{"name":"CONACyT-Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Interior Internado Palmira S\/N, Col. Palmira, C.P. 62490 Cuernavaca, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Art and Sciences, Cankaya University, 06530 Ankara, Turkey"},{"name":"Institute of Space Sciences, P.O. Box, MG-23, R 76900 Magurele-Bucharest, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7855-508X","authenticated-orcid":false,"given":"Fairouz","family":"Tchier","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Saud University, P.O. BOX 2454, Riyadh 11451, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,20]]},"reference":[{"key":"ref_1","first-page":"14","article-title":"A fractional model of Navier-Stokes equation arising in unsteady flow of a viscous fluid","volume":"17","author":"Kumar","year":"2015","journal-title":"J. Assoc. Arab Univ. Basic Appl. Sci."},{"key":"ref_2","first-page":"340","article-title":"New numerical approximations for space-time fractional Burgers\u2019 equations via a Legendre spectral-collocation method","volume":"67","author":"Bhrawy","year":"2015","journal-title":"Rom. Rep. 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