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

Entropy

José Francisco Gómez-Aguilar¹  Ricardo Fabricio Escobar-Jiménez²  Dumitru Baleanu³  Maysaa Mohamed Al Qurashi⁴  Marco Antonio Taneco-Hernández⁵  Victor Fabian Morales-Delgado⁵ 

[1] CONACYT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca 62490, Mexico;Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca 62490, Mexico;Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, Ankara 06530, Turkey;Mathematics Department, King Saud University, Riyadh 12364, Saudi Arabia;Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo 39087, Mexico;

关键词: fractional-order circuits;    Liouville–Caputo fractional operator;    Caputo–Fabrizio fractional operator;    Atangana–Baleanu fractional operator;   

DOI  :  10.3390/e18080402

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown