# A Fractional LC − RC Circuit

• Volume: 9, Issue: 1, page 33-41
• ISSN: 1311-0454

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## Abstract

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Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05We 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.

## How to cite

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Ayoub, N., et al. "A Fractional LC − RC Circuit." Fractional Calculus and Applied Analysis 9.1 (2006): 33-41. <http://eudml.org/doc/11307>.

@article{Ayoub2006,
abstract = {Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05We 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.},
author = {Ayoub, N., Alzoubi, F., Khateeb, H., Al-Qadi, M., Hasan (Qaseer), M., Albiss, B., Rousan, A.},
journal = {Fractional Calculus and Applied Analysis},
keywords = {30B10; 33B15; 44A10; 47N70; 94C05; 26A33},
language = {eng},
number = {1},
pages = {33-41},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {A Fractional LC − RC Circuit},
url = {http://eudml.org/doc/11307},
volume = {9},
year = {2006},
}

TY - JOUR
AU - Ayoub, N.
AU - Alzoubi, F.
AU - Khateeb, H.
AU - Hasan (Qaseer), M.
AU - Albiss, B.
AU - Rousan, A.
TI - A Fractional LC − RC Circuit
JO - Fractional Calculus and Applied Analysis
PY - 2006
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 9
IS - 1
SP - 33
EP - 41
AB - Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05We 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.
LA - eng
KW - 30B10; 33B15; 44A10; 47N70; 94C05; 26A33
UR - http://eudml.org/doc/11307
ER -

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