Investigación

 

A physical interpretation of fractional calculus in observables terms: analysis of the fractional time constant and the transitory response

 

J.F. Gómez-Aguilar^a,*, R. Razo-Hernández^b, and D. Granados-Lieberman^b

 

ª Departamento de Ingeniería Eléctrica, División de Ingenierías Campus Irapuato-Salamanca, Universidad de Guanajuato Carretera Salamanca-Valle de Santiago, km. 3.5 + 1.8 km Comunidad de Palo Blanco, Salamanca Guanajuato. México, * Tel: (464) 6479940 e-mail: jgomez@ugto.mx

^b Departamento de Electromecánica, Instituto Superior de Irapuato, Irapuato, Guanajuato, México, e-mail: jorazo@itesi.edu.mx, david.granados@itesi.edu.mx

 

Received 17 June 2013.
Accepted 9 September 2013.

 

Abstract

This work presents the analysis of the fractional time constant and the transitory response (delay, rise, and settling times) of a RC circuit as a physical interpretation of fractional calculus in observables terms, the definition of Caputo fractional derivative is applied. The physical interpretation of these observables allows a clearer understanding of the concept of fractional derivative.

Keywords: Fractional calculus; fractional time constant; fractional differential equations; transitory response.

 

Resumen

Este trabajo presenta el análisis de la constante de tiempo transitoria y de la respuesta en frecuencia (tiempo de retraso, elevación y asentamiento) de un circuito RC como una interpretación física del cálculo fraccionario en términos de estos observables, la definición de derivada fraccionaria de Caputo es aplicada. La interpretación física de estos observables permite tener un entendimiento claro del concepto de derivada fraccionaria.

Descriptores: Calculo fraccionario; constante de tiempo fraccionaria; ecuaciones diferenciales fraccionarias; respuesta transitoria.

 

PACS: 03.50.De; 45.10.Hj; 05.45.-a

 

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