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

• Published in: Entropy (Basel, Switzerland) Vol. 18; no. 8; p. 402
• Main Authors: Gómez-Aguilar, José, Morales-Delgado, Victor, Taneco-Hernández, Marco, Baleanu, Dumitru, Escobar-Jiménez, Ricardo, Al Qurashi, Maysaa
• Format: Journal Article
• Language: English
• Published: MDPI AG 20.08.2016
• Subjects: Atangana–Baleanu fractional operator; Caputo–Fabrizio fractional operator; fractional-order circuits; Liouville–Caputo fractional operator
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e18080402

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.