Investigation of electrical RC circuit within the framework of fractional calculus

Abstract

In this paper, charging and discharging processes of different capacitors in electrical RC circuit are considered theoretically and experimentally. The non-local behaviors in these processes, arising from the time fractality, are investigated via fractional calculus. In this context, the time fractional differential equation related to electrical RC circuit is proposed by making use of Caputo fractional derivative. The resulting solution exhibits a feature in between power law and exponential law forms, and is obtained in terms of Mittag-Leffler function which describes physical systems with memory. The order of fractional derivative characterizes the fractality of time and being considered in the interval $0<\alpha \leq 1$. The traditional conclusions are recovered for $\alpha =1$, where time becomes homogenous and system has Markovian nature. By using time fractional approach, the discrepancies between the experimentally measured data and the theoretical calculations have been removed.