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Advances in Mathematical Physics
Volume 2016, Article ID 9720181, 15 pages
http://dx.doi.org/10.1155/2016/9720181
Research Article

Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel

1CONACYT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Colonia Palmira, 62490 Cuernavaca, MOR, Mexico
2Facultad de Ingeniería Mecánica y Eléctrica, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, Mexico
3Facultad de Ingeniería Electrónica y Comunicaciones, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, Mexico

Received 2 February 2016; Accepted 26 April 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

We present an alternative representation of integer and fractional electrical elements in the Laplace domain for modeling electrochemical systems represented by equivalent electrical circuits. The fractional derivatives considered are of Caputo and Caputo-Fabrizio type. This representation includes distributed elements of the Cole model type. In addition to maintaining consistency in adjusted electrical parameters, a detailed methodology is proposed to build the equivalent circuits. Illustrative examples are given and the Nyquist and Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. The advantage of our representation appears according to the comparison between our model and models presented in the paper, which are not physically acceptable due to the dimensional incompatibility. The Markovian nature of the models is recovered when the order of the fractional derivatives is equal to 1.