A new RLC series-resonant circuit modeled by local fractional derivative

Abstract

The local fractional derivative has gained more and more attention in the field of fractal electrical circuits. In this paper, we propose a new ?-order RLC** resonant circuit described by the local fractional derivative for the first time. By studying the non-differentiable lumped elements, the non-differentiable equivalent imped?ance is obtained with the help of the local fractional Laplace transform. Then the non-differentiable resonant angular frequency is studied and the non-differentiable resonant characteristic is analyzed with different input signals and parameters, where it is observed that the ?-order RLC resonant circuit becomes the ordinary one for the special case when the fractional order ? = 1. The obtained results show that the local fractional derivative is a powerful tool in the description of fractal circuit systems.