Comportamiento de orden fraccionario en la respuesta de un circuito RC mediante derivada de núcleo singular
DOI:
https://doi.org/10.29105/ingenierias24.91-19Palabras clave:
Circuito electrónico RC, cálculo fraccionario, solución analítica, derivada tipo CaputoResumen
En este artículo, se presenta la ecuación diferencial fraccionaria de un circuito electrónico RC en términos de la derivada fraccionaria de tipo Caputo y la solución analítica exacta usando propiedades de la transformada de Laplace y la función Mittag-Leffler. El orden de la derivada fraccionaria es definido en el intervalo 0<q≤1, preservando la dimensionalidad de los parámetros R y C. Además, se muestra la respuesta experimental del circuito propuesto y se compara con las soluciones analíticas. Los resultados muestran que el voltaje del capacitor depende directamente de los valores del orden fraccionario.
Descargas
Citas
D. Baleanu, K. Diethelm, E. Scalas and J. Trujillo, Fractional Calculus: Models and Numerical Methods, London: World Scientific Publishing, 2017. DOI: https://doi.org/10.1142/10044
H. Su, Y. Zhang, D. Baleanu, W. Chen and Y. Chen, “A new collection of real world applications of fractional calculus in science and engineering,” Communications in Nonlinear Science and Numerical Simulation, vol. 64, pp. 213-231, 2018. DOI: https://doi.org/10.1016/j.cnsns.2018.04.019
M. Tavazoei, “Fractional order chaotic systems: history, achievements, applications, and future challenges,” The European Physical Journal Special Topics, vol. 229, pp. 887-904, 2020. DOI: https://doi.org/10.1140/epjst/e2020-900238-8
I. Podlubny, Fractional Differential Equations, New York: Academic Press, 1998.
M. Caputo and M. Fabrizio, “A new Definition of Fractional Derivative without singular kernel,” Progress in Fractional Differentiation and Applications, vol. 1, no. 2, pp. 73-85, 2015.
A. Atangana and D. Baleanu, “New fractional derivatives with non-local and non-singular kernel,” Thermal Science, vol. 20, no. 2, pp. 763-769, 2016. DOI: https://doi.org/10.2298/TSCI160111018A
R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, “A new definition of fractional derivative,” Journal of Computational and Applied Mathematics, vol. 264, pp. 65-70, 2014. DOI: https://doi.org/10.1016/j.cam.2014.01.002
J. Munoz-Pacheco, C. Posadas-Castillo and E. Zambrano-Serrano, “The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation,” Symmetry, vol. 12, no. 9, p. 1395, 2020. DOI: https://doi.org/10.3390/sym12091395
J. Rosales, J. Filoteo and G. A, “A comparative analysis of the RC circuit with local and non-local fractional derivatives,” Revista Mexicana de Fisica, vol. 64, no. 6, pp. 647-654, 2018. DOI: https://doi.org/10.31349/RevMexFis.64.647
J. Gómez-Aguilar, “Fundamental solutions to electrical circuits of non-integer order via fractional derivatives with and without singular kernels,” The European Physical Journal Plus volume, vol. 133, p. 197, 2018. DOI: https://doi.org/10.1140/epjp/i2018-12018-x
N. Sene, “Stability analysis of electrical RLC circuit described by the Caputo-Liouville generalized fractional derivative,” Alexandria Engineering Journal, vol. 59, pp. 2083-2090, 2020. DOI: https://doi.org/10.1016/j.aej.2020.01.008
N. Sene, “Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivative,” AIMS Mathemathics, vol. 4, no. 1, pp. 147-165, 2019. DOI: https://doi.org/10.3934/Math.2019.1.147
J. Gómez-Aguilar, J. Rosales-Garcia, J. Razo-Hernandez and G.-C. M, “Fractional RC and LC electrical circuits,” Ingenierias Investigación y Tecnología , vol. 15, no. 2, pp. 311-319, 2014. DOI: https://doi.org/10.1016/S1405-7743(14)72219-X
M. Kenneth and B. Ross, An Introduction to the fractional Calculus and Fractional Differential Equations, Wiley-Blackwell, 1993.
Descargas
Publicado
Cómo citar
Número
Sección
Datos de los fondos
-
Consejo Nacional de Ciencia y Tecnología
Números de la subvención 350385;66654, A1-S-31628
