Servicios Personalizados
Revista
Articulo
Indicadores
- Citado por SciELO
- Accesos
Links relacionados
- Similares en SciELO
Compartir
Revista mexicana de física
versión impresa ISSN 0035-001X
Rev. mex. fis. vol.62 no.2 México mar./abr. 2016
Investigación
Electrical circuits described by a fractional derivative with regular Kernel
J.F. Gómez-Aguilara*, T. Córdova-Fragab, J.E. Escalante-Martínezc, C. Calderón-Ramónc, and R.F. Escobar-Jiménezd
a* Catedrático del Consejo Nacional de Ciencia y Tecnología-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México. Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, Morelos, México.
6 Departamento de Ingeniería Física, División de Ciencias e Ingenierías Campus León, Universidad de Guanajuato, León, Guanajuato, México.
c Facultad de Ingeniería Mecánica y Eléctrica. Universidad Veracruzana. Av. Venustiano Carranza S/N, Col. Revolución, 93390, Poza Rica Veracruz, México.
d Centro Nacional de Investigación y Desarrollo Tecnológico Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México. * e-mail: jgomez@cenidet.edu.mx
Received 3 August 2015;
accepted 10 December 2015
Abstract
In this paper we presented the electrical circuits LC, RC, RL and RLC using a novel fractional derivative with regular kernel called Caputo-Fabrizio fractional derivative. The fractional equations in the time domain considers derivatives of order (0; 1], the analysis is performed in the frequency domain and the conversion in the time domain is performed using the numerical inverse Laplace transform algorithm; furthermore, analytical solutions are presented for these circuits considering different source terms introduced in the fractional equation. The numerical results for different values of the fractional order γ exhibits fluctuations or fractality of time in different scales and the existence of heterogeneities in the electrical components causing irreversible dissipative effects. The classical behaviors are recovered when the order of the temporal derivative is equal to 1 and the system exhibit the Markovian nature.
Keywords: Electrical circuits; Caputo-Fabrizio fractional derivative; fractional-order circuits; oscillations.
PACS: 84.30.Bv; 84.32.Ff; 84.32.Tt
DESCARGAR ARTÍCULO EN FORMATO PDF
References
1. M. de Wild, W. Pomp, G.H. Koenderink, Biophysical Journal, 105 (2013)200-210. [ Links ]
2. Sungho Kim et al., Physical electro-thermal model of resistive switching in bi-layered resistance-change memory. Scientific Reports 3, Article number: 1680, doi:10.1038/srep01680. [ Links ]
3. C.H. Henager, W.T. Pawlewicz, Thermal conductivities of thin, sputtered optical films. Applied Optics, 32 (1993) 91-101. [ Links ]
4. D. Baleanu, Z.B. Gunvenc and J.A. Tenreiro Machado, New Trends in Nanotechnology and Fractional Calculus Applications. Springer, (2010). [ Links ]
5. V.E. Tarasov, Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media. Springer Science & Business Media, (2011). [ Links ]
6. J.F. Gómez Aguilar and M. Miranda Hernández, Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative. Abstract and Applied Analysis, 2014, Article ID 283019, 8 pages, (2014). doi:10.1155/2014/283019 [ Links ]
7. V. Mishra, K. Vishal, S. Das and S.H. Ong, Z. Naturforsch 69a (2014) 135-144. [ Links ]
8. J.F. Gómez Aguilar, D. Baleanu, Proceedings of the Romanian Academy, Series A. 1-15 (2014) 27-34. [ Links ]
9. T.M. Atanackovic, S. Pilipovic, B. Stankovic, D. Zorica, Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes. Wiley, London (2014). [ Links ]
10. J.F. Gómez Aguilar and D. Baleanu, Z. Naturforsch. 69 (2014) 539-546. Doi:10.5560/ZNA.2014-0049. [ Links ]
11. S. Kumar, Z. Naturforsch. 68 (2013) 777-784. [ Links ]
12. H. Samavati, A. Hajimiri, A.R. Shahani, G.N. Nasserbakht, T.H. Lee, IEEE Journal of Solid-State Circuits 33 (1998) 2035-2041. [ Links ]
13. S.I. Ravello Arias, D. Ramirez Muñoz, J. Sánchez Moreno, S. Cardoso, R. Ferreira and P.J. Peixeiro de Freitas, Sensors 13 (2013) 17516-17533. doi:10.3390/s131217516, [ Links ].
14. J.F. Gómez Aguilar, Behavior Characteristic of a Cap-Resistor, Memcapacitor and a Memristor from the Response Obtained of RC and RL Electrical Circuits Described by Fractional Differential Equations. Turkish Journal of Electrical Engineering & Computer Sciences. Accepted for publication.
15. R. Caponetto, G. Dongola, G. Maione, A. Pisano, Journal of Vibration and Control. 20 (2014) 1066-1075. [ Links ]
16. A.S. Elwakil, Circuits and Systems Magazine, IEEE 10.4 (2010) 40-50. [ Links ]
17. F. Gómez, J. Rosales, M. Guía, Cent. Eur. J. Phys. Springer. (2013). [ Links ]
18. M. Guía, F. Gómez, J. Rosales, Cent. Eur. J. Phys. Springer. (2013). [ Links ]
19. F. Gómez-Aguilar, R. Razo-Hernández, J. Rosales-García, M. Guía-Calderón, Revista de Ingeniería, Investigación y Tecnología, UNAM. 2 (2014) 311-319. [ Links ]
20. A. Obeidat, M. Gharibeh, M. Al-Ali, A. Rousan, Fract. Calc. App. Anal 14, Springer (2011). [ Links ]
21. J.F. Gómez-Aguilar, R. Razo-Hernández, D. Granados-Lieberman, Rev. Mex. Fis. 60 (2014) 32-38. [ Links ]
22. H. Ertik, A.E. Calik, H. Sirin, M.Sen, B. Ãder, Rev. Mex. Fis. 61 (2015) 58-63. [ Links ]
23. J. Valsa, J. Vlach, International Journal of Circuit Theory and Applications 41 (2013) 59-67. [ Links ]
24. J. Chen, Z. Zeng, P. Jiang, Neural Networks 51 (2014) 1-8. [ Links ]
25. A.A. Rousan et al., Fractional Calculus and Applied analysis, 9 (2006)33-41. [ Links ]
26. K.B. Oldham and J. Spanier, The Fractional Calculus. Academic Press, New York, (1974). [ Links ]
27. A. Atangana, A. Secer, Abstract and Applied Analysis 2013 (2013). Doi:10.1155/2013/279681. [ Links ]
28. K. Diethelm, The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type (Springer-Verlag, Berlin, Heidelberg,2010). [ Links ]
29. K. Diethelm, N.J. Ford, A.D. Freed, Yu. Luchko, Comp. Methods in Appl. Mech. and Eng. 194 (2005) 743-773. [ Links ]
30. D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos. World Scientific, (2012). [ Links ]
31. I. Podlubny, Fractional Differential Equations. Academic Press, New York, (1999). [ Links ]
32. A. Atangana, B.S.T. Alkahtani, Entropy 17 (2015) 4439-4453. [ Links ]
33. M. Caputo, M. Fabricio, Progr. Fract. Differ. Appl. 1 (2015) 73-85. [ Links ]
34. J. Lozada, J.J. Nieto, Progr. Fract. Differ. Appl. 1 (2015) 87-92. [ Links ]
35. A. Atangana, J.J. Nieto, Advances in Mechanical Engineering, 7 (2015) 1-6. [ Links ]
36. A. Atangana, B.S.T. Alkahtani, Advances in Mechanical Engineering, 7 (2015) 1-6. [ Links ]
37. H. Batarfi, J. Losada, J.J. Nieto, W. Shammakh, Journal of Function Spaces (2015). [ Links ]
38. J.F. Gómez-Aguilar et al., Entropy 17 (2015) 6289-6303. [ Links ]
39. J.G. Proakis and D.G. Manolakis, Digital Signal Processing, in Principles, Algorithms and Applications. 3rd ed. Upper Saddle River, NJ: Prentice-Hall, (1996). [ Links ]
40. D.J. Wilcox, I.S. Gibson, Int. J. Numer. Methods Eng. 20 (1984) 1507-1519. [ Links ]
41. P. Moreno, A. Ramirez, IEEE Trans. Power Delivery. 23 (2008) 2599-2609. [ Links ]
42. H. Sheng, Y. Li, Y. Chen, Journal of the Franklin Institute 348 (2011)315-330. [ Links ]
43. J.F. Gómez-Aguilar, J.J. Rosales-García, J.J. Bernal-Alvarado, T. Córdova-Fraga, R. Guzmán-Cabrera, Rev. Mex. Fis 58 (2012) 524-537. [ Links ]