A Fractional LC − RC Circuit
Fractional calculus and applied analysis, Tome 9 (2006) no. 1, pp. 33-41
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
We suggest a fractional differential equation that combines the simple
harmonic oscillations of an LC circuit with the discharging of an RC circuit.
A series solution is obtained for the suggested fractional differential
equation. When the fractional order α = 0, we get the solution for the RC
circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary
α we get a general solution which shows how the oscillatory behavior
(LC circuit) go over to a decay behavior (RC circuit) as grows from 0 to
1, and vice versa. An explanation of the behavior is proposed based on the
idea of the evolution of a resistive property in the inductor giving a new
value to the inductance that affects the frequency of the oscillator.
Keywords:
Fractional Calculus, Differintegration, Fractional Differential Equation, Simple Harmonic Oscillator, Damping, Series Solution, LCR Circuit, Intermediate Stages, 30B10, 33B15, 44A10, 47N70, 94C05, 26A33
@article{FCAA_2006_9_1_a2,
author = {Ayoub, N. and Alzoubi, F. and Khateeb, H. and Al-Qadi, M. and Hasan (Qaseer), M. and Albiss, B. and Rousan, A.},
title = {A {Fractional} {LC} \ensuremath{-} {RC} {Circuit}},
journal = {Fractional calculus and applied analysis},
pages = {33--41},
publisher = {mathdoc},
volume = {9},
number = {1},
year = {2006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/FCAA_2006_9_1_a2/}
}
TY - JOUR AU - Ayoub, N. AU - Alzoubi, F. AU - Khateeb, H. AU - Al-Qadi, M. AU - Hasan (Qaseer), M. AU - Albiss, B. AU - Rousan, A. TI - A Fractional LC − RC Circuit JO - Fractional calculus and applied analysis PY - 2006 SP - 33 EP - 41 VL - 9 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FCAA_2006_9_1_a2/ LA - en ID - FCAA_2006_9_1_a2 ER -
%0 Journal Article %A Ayoub, N. %A Alzoubi, F. %A Khateeb, H. %A Al-Qadi, M. %A Hasan (Qaseer), M. %A Albiss, B. %A Rousan, A. %T A Fractional LC − RC Circuit %J Fractional calculus and applied analysis %D 2006 %P 33-41 %V 9 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/FCAA_2006_9_1_a2/ %G en %F FCAA_2006_9_1_a2
Ayoub, N.; Alzoubi, F.; Khateeb, H.; Al-Qadi, M.; Hasan (Qaseer), M.; Albiss, B.; Rousan, A. A Fractional LC − RC Circuit. Fractional calculus and applied analysis, Tome 9 (2006) no. 1, pp. 33-41. http://geodesic.mathdoc.fr/item/FCAA_2006_9_1_a2/