RLC electrical circuit of non-integer order

摘要

In this work a fractional differential equation for the electrical RLC circuit is studied. The order of the derivative being considered is 0 < γ ≤1. an auxiliary parameter To keep the dimensionality of the physical quantities R;Land C is introduced. This parameter characterizes the existence of fractional components in the system. It is shown that there is a relation between γ and σ through the physical parameters of the circuit. Due to this relation, the analytical solution is given in terms of the Mittag-Leffler funcRtiLoCn depending on the order of the fractional differential equation.