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Advances in Mathematical Physics
Volume 2016, Article ID 9740410, 8 pages
http://dx.doi.org/10.1155/2016/9740410
Research Article

On the Possibility of the Jerk Derivative in Electrical Circuits

1CONACYT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, 62490 Cuernavaca, MOR, Mexico
2Departamento de Ingeniería Electrica, DICIS, Universidad de Guanajuato, Carretera Salamanca-Valle de Santiago, Km. 3.5 + 1.8 Km., Comunidad de Palo Blanco, Salamanca, GTO, Mexico
3Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, MOR, Mexico

Received 28 June 2016; Revised 15 August 2016; Accepted 22 September 2016

Academic Editor: Alexander Iomin

Copyright © 2016 J. F. Gómez-Aguilar et al. 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.

Abstract

A subclass of dynamical systems with a time rate of change of acceleration are called Newtonian jerky dynamics. Some mechanical and acoustic systems can be interpreted as jerky dynamics. In this paper we show that the jerk dynamics are naturally obtained for electrical circuits using the fractional calculus approach with order . We consider fractional LC and RL electrical circuits with for different source terms. The LC circuit has a frequency dependent on the order of the fractional differential equation , since it is defined as , where is the fundamental frequency. For , the system is described by a third-order differential equation with frequency , and assuming the dynamics are described by a fourth differential equation for jerk dynamics with frequency .