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Title: A Fractional LC − RC Circuit
Authors: Ayoub, N.
Alzoubi, F.
Khateeb, H.
Al-Qadi, M.
Hasan (Qaseer), M.
Albiss, B.
Rousan, A.
Keywords: Fractional Calculus
Fractional Differential Equation
Simple Harmonic Oscillator
Series Solution
LCR Circuit
Intermediate Stages
Issue Date: 2006
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 9, No 1, (2006), 33p-41p
Abstract: 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.
Description: Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05
ISSN: 1311-0454
Appears in Collections:2006

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