{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T06:41:16Z","timestamp":1788417676991,"version":"build-2803163510"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2016,8,20]],"date-time":"2016-08-20T00:00:00Z","timestamp":1471651200000},"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 we obtain analytical solutions for the electrical RLC circuit model defined with Liouville\u2013Caputo, Caputo\u2013Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are considered in the fractional differential equations. The classical behaviors are recovered when the fractional order \u03b1 is equal to 1.<\/jats:p>","DOI":"10.3390\/e18080402","type":"journal-article","created":{"date-parts":[[2016,8,22]],"date-time":"2016-08-22T10:40:33Z","timestamp":1471862433000},"page":"402","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":95,"title":["Analytical Solutions of the Electrical RLC Circuit via Liouville\u2013Caputo Operators with Local and Non-Local Kernels"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9403-3767","authenticated-orcid":false,"given":"Jos\u00e9","family":"G\u00f3mez-Aguilar","sequence":"first","affiliation":[{"name":"CONACYT-Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Tecnol\u00f3gico Nacional de M\u00e9xico, Interior Internado Palmira S\/N, Col. Palmira, Cuernavaca 62490, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Victor","family":"Morales-Delgado","sequence":"additional","affiliation":[{"name":"Unidad Acad\u00e9mica de Matem\u00e1ticas, Universidad Aut\u00f3noma de Guerrero, Av. L\u00e1zaro C\u00e1rdenas S\/N, Cd. Universitaria, Chilpancingo 39087, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marco","family":"Taneco-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Unidad Acad\u00e9mica de Matem\u00e1ticas, Universidad Aut\u00f3noma de Guerrero, Av. L\u00e1zaro C\u00e1rdenas S\/N, Cd. Universitaria, Chilpancingo 39087, 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 and Computer Science, Faculty of Art and Sciences, Cankaya University, Ankara 06530, Turkey"},{"name":"Institute of Space Sciences, P.O. Box MG-23, Magurele-Bucharest RO-76900, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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, Interior Internado Palmira S\/N, Col. Palmira, Cuernavaca 62490, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0979-5746","authenticated-orcid":false,"given":"Maysaa","family":"Al Qurashi","sequence":"additional","affiliation":[{"name":"Mathematics Department, King Saud University, Riyadh 12364, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2016,8,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kaczorek, T., and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Springer.","DOI":"10.1007\/978-3-319-11361-6"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40243-015-0052-y","article-title":"Fractional-order models of supercapacitors, batteries and fuel cells: A survey","volume":"4","author":"Freeborn","year":"2015","journal-title":"Mater. Renew. Sustain. 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