Fractional RC and LC Electrical Circuits
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Universidad Nacional Autónoma de México
2014
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| _version_ | 1876440738000011264 |
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| author | José Francisco Gómez-Aguilar |
| author_facet | José Francisco Gómez-Aguilar |
| contents | Fractional RC and LC Electrical Circuits José Francisco Gómez-Aguilar Juan Rosales-García José Roberto Razo-Hernández Manuel Guía-Calderón Ingeniería mittag leffler functions • electrical circuits • fractional calculus • fractional structures In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < ≤ 1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structu- res in the system. A relation between the fractional order time derivative and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of . The classical cases are re- covered by taking the limit when = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations. 2014 artículo científico 1405-7743 https://www.redalyc.org/articulo.oa?id=40430749013 en http://www.redalyc.org/revista.oa?id=404 Ingeniería. Investigación y Tecnología application/pdf Universidad Nacional Autónoma de México Ingeniería. Investigación y Tecnología (México) Num.2 Vol.XV |
| format | Artículo científico |
| id | redalyc_40430749013 |
| institution | Redalyc |
| language | en |
| publishDate | 2014 |
| publisher | Universidad Nacional Autónoma de México |
| spellingShingle | Fractional RC and LC Electrical Circuits José Francisco Gómez-Aguilar Ingeniería mittag leffler functions • electrical circuits • fractional calculus • fractional structures Fractional RC and LC Electrical Circuits José Francisco Gómez-Aguilar Juan Rosales-García José Roberto Razo-Hernández Manuel Guía-Calderón Ingeniería mittag leffler functions • electrical circuits • fractional calculus • fractional structures In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < ≤ 1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structu- res in the system. A relation between the fractional order time derivative and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of . The classical cases are re- covered by taking the limit when = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations. 2014 artículo científico 1405-7743 https://www.redalyc.org/articulo.oa?id=40430749013 en http://www.redalyc.org/revista.oa?id=404 Ingeniería. Investigación y Tecnología application/pdf Universidad Nacional Autónoma de México Ingeniería. Investigación y Tecnología (México) Num.2 Vol.XV |
| title | Fractional RC and LC Electrical Circuits |
| topic | Ingeniería mittag leffler functions • electrical circuits • fractional calculus • fractional structures |
| url | https://www.redalyc.org/articulo.oa?id=40430749013 |