# A Fractional LC − RC Circuit

Ayoub, N.; Alzoubi, F.; Khateeb, H.; Al-Qadi, M.; Hasan (Qaseer), M.; Albiss, B.; Rousan, A.

Fractional Calculus and Applied Analysis (2006)

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

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topAyoub, 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 - 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

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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