Treatment of Nonlinear Electrical Circuits by the Caputo-Fabrizio Derivative

Authors Z. Korichi1 , A. Souigat1 , Y. Benkrima1 , M.T. Meftah2

1Ecole Normale Supérieure de Ouargla, 30000 Ouargla, Algeria

2Laboratoire LRPPS, Faculté de Mathématiques et Sciences de la Matière, Université Kasdi-Merbah, Ouargla 30000, Algeria

Issue Volume 14, Year 2022, Number 4
Dates Received 15 May 2022; revised manuscript received 10 August 2022; published online 25 August 2022
Citation Z. Korichi, A. Souigat, et al., J. Nano- Electron. Phys. 14 No 4, 04014 (2022)
PACS Number(s) 02.90. + p, 45.10.Hj
Keywords Fractional differential equations, Fractional derivative, Caputo-Fabrizio fractional derivative, Fractional electrical circuits.

Caputo and Fabrizio have recently proposed a new fractional order derivative without singular kernel, which is suitable for the Laplace transform and has many interesting properties that motivated its use to solve and model many phenomena in various branches of science. In our work, we have treated the fractional differential equations of nonlinear electrical circuits by using the definition of Caputo-Fabrizio derivative. Indeed, we have transformed the fractional differential equations, describing RC, RL and LC circuits, into an ordinary order differential equation. Then we have determined explicit solutions to these differential equations. For the RC circuit, we studied changes in charge with time and with derivative order and we found that for all values, the curve retains its general shape. In contrast to the time constant, which increases as alpha increases, we established that q0 has no relationship to. For the RL circuit, time variations of electric current are investigated for various alpha values, and we found that the maximum current I0 does not change with derivative order. Also, for the LC circuit, we studied charge changes for various alpha values, and we showed that the shape of the LC vibration is related to the derivative order. For the LC circuit, the vibration is a sine wave, and the RC circuit vibration is a damped vibration. To validate our obtained results, we found the familiar results.

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