Geodesic
A Fractional LC − RC Circuit
Fractional calculus and applied analysis, Tome 9 (2006) no. 1, pp. 33-41.

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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 
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     title = {A {Fractional} {LC} \ensuremath{-} {RC} {Circuit}},
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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/