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Entropy 2016, 18(8), 402; doi:10.3390/e18080402

Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels

1
CONACYT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca 62490, Mexico
2
Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo 39087, Mexico
3
Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, Ankara 06530, Turkey
4
Institute of Space Sciences, P.O. Box MG-23, Magurele-Bucharest RO-76900, Romania
5
Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca 62490, Mexico
6
Mathematics Department, King Saud University, Riyadh 12364, Saudi Arabia
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 22 June 2016 / Revised: 9 August 2016 / Accepted: 17 August 2016 / Published: 20 August 2016
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
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Abstract

In this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville–Caputo, Caputo–Fabrizio 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 α is equal to 1. View Full-Text
Keywords: fractional-order circuits; Liouville–Caputo fractional operator; Caputo–Fabrizio fractional operator; Atangana–Baleanu fractional operator fractional-order circuits; Liouville–Caputo fractional operator; Caputo–Fabrizio fractional operator; Atangana–Baleanu fractional operator
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Gómez-Aguilar, J.F.; Morales-Delgado, V.F.; Taneco-Hernández, M.A.; Baleanu, D.; Escobar-Jiménez, R.F.; Al Qurashi, M.M. Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels. Entropy 2016, 18, 402.

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