{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:43:17Z","timestamp":1772293397653,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,1,28]],"date-time":"2017-01-28T00:00:00Z","timestamp":1485561600000},"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>In this work, the study of the fractional behavior of the Bateman\u2013Feshbach\u2013Tikochinsky and Caldirola\u2013Kanai oscillators by using different fractional derivatives is presented. We obtained the Euler\u2013Lagrange and the Hamiltonian formalisms in order to represent the dynamic models based on the Liouville\u2013Caputo, Caputo\u2013Fabrizio\u2013Caputo and the new fractional derivative based on the Mittag\u2013Leffler kernel with arbitrary order \u03b1. Simulation results are presented in order to show the fractional behavior of the oscillators, and the classical behavior is recovered when \u03b1 is equal to 1.<\/jats:p>","DOI":"10.3390\/e19020055","type":"journal-article","created":{"date-parts":[[2017,1,30]],"date-time":"2017-01-30T11:36:30Z","timestamp":1485776190000},"page":"55","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":52,"title":["Bateman\u2013Feshbach Tikochinsky and Caldirola\u2013Kanai Oscillators with New Fractional Differentiation"],"prefix":"10.3390","volume":"19","author":[{"given":"Antonio","family":"Coronel-Escamilla","sequence":"first","affiliation":[{"name":"Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Tecnol\u00f3gico Nacional de M\u00e9xico, 62490 Cuernavaca, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9403-3767","authenticated-orcid":false,"given":"Jos\u00e9","family":"G\u00f3mez-Aguilar","sequence":"additional","affiliation":[{"name":"CONACyT-Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Tecnol\u00f3gico Nacional de M\u00e9xico, 62490 Cuernavaca, Mexico"}]},{"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, 0630 Ankara, Turkey"},{"name":"Institute of Space Sciences, 409 Atomistilor Str., 077125 Magurele, Romania"}]},{"given":"Teodoro","family":"C\u00f3rdova-Fraga","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda F\u00edsica, Divisi\u00f3n de Ciencias e Ingenier\u00edas Campus Le\u00f3n, Universidad de Guanajuato, 37328 Le\u00f3n, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3367-6552","authenticated-orcid":false,"given":"Ricardo","family":"Escobar-Jim\u00e9nez","sequence":"additional","affiliation":[{"name":"Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Tecnol\u00f3gico Nacional de M\u00e9xico, 62490 Cuernavaca, Mexico"}]},{"given":"Victor","family":"Olivares-Peregrino","sequence":"additional","affiliation":[{"name":"Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Tecnol\u00f3gico Nacional de M\u00e9xico, 62490 Cuernavaca, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0979-5746","authenticated-orcid":false,"given":"Maysaa","family":"Qurashi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Saud University, 11451 Riyadh, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,28]]},"reference":[{"key":"ref_1","first-page":"452","article-title":"Decoherence of quantum damped oscillators","volume":"43","author":"Kim","year":"2003","journal-title":"Phys. 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