Electrical circuits described by a fractional derivative with regular Kernel

Abstract

In this paper we presented the electrical circuits LC, RC, RL and RLC using a novel fractional derivative with regular kernel called Caputo-Fabrizio fractional derivative. The fractional equations in the time domain considers derivatives of order $(0;1]$, the analysis is performed in the frequency domain and the conversion in the time domain is performed using the numerical inverse Laplace transform algorithm; furthermore, analytical solutions are presented for these circuits considering different source terms introduced in the fractional equation. The numerical results for different values of the fractional order $\gamma$ exhibits fluctuations or fractality of time in different scales and the existence of heterogeneities in the electrical components causing irreversible dissipative effects. The classical behaviors are recovered when the order of the temporal derivative is equal to 1 and the system exhibit the Markovian nature.