Analysis of charge variation in fractional order LC electrical circuit

Abstract

In this paper, the charge variation in time has been investigated in electrical LC circuit within the framework of fractional calculus. The second order differential equation related to the LC circuit has been re-solved by using Caputo fractional derivative. The solution of this new equation has been obtained in terms of Mittag-Leffler function which behaves in between power law and exponential law forms. The order of time-fractional derivative characterizes the time fractality effects in the system, and is considered in the interval $1<\alpha \leq 2$. The obtained results have been compared with the other studies in the literature. It has been concluded that the Mittag-Leffler function and the order of time-fractional derivative have a special importance to take into account the non-local behaviour of the physical process in time.