Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels
José Francisco Gómez-Aguilar,
Victor Fabian Morales-Delgado,
Marco Antonio Taneco-Hernández,
Dumitru Baleanu,
Ricardo Fabricio Escobar-Jiménez,
Maysaa Mohamed Al Qurashi
Affiliations
José Francisco Gómez-Aguilar
CONACYT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca 62490, Mexico
Victor Fabian Morales-Delgado
Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo 39087, Mexico
Marco Antonio Taneco-Hernández
Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo 39087, Mexico
Dumitru Baleanu
Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, Ankara 06530, Turkey
Ricardo Fabricio Escobar-Jiménez
Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca 62490, Mexico
Maysaa Mohamed Al Qurashi
Mathematics Department, King Saud University, Riyadh 12364, Saudi Arabia
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.
