Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1270

 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 CalculusDifferintegrationFractional Differential EquationSimple Harmonic OscillatorDampingSeries SolutionLCR CircuitIntermediate Stages30B1033B1544A1047N7094C0526A33 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 URI: http://hdl.handle.net/10525/1270 ISSN: 1311-0454 Appears in Collections: 2006

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