Abstract
•A fractal model of the LC-electric circuit is derived from local fractional calculus.•The relaxation oscillator in the fractal LC-electric circuit is considered.•The exact solution for the model is analyzed by the local fractional Laplace transform.•Comparative results among the different operators are presented.
A non-differentiable model of the LC-electric circuit described by a local fractional differential equation of fractal dimensional order is addressed in this article. From the fractal electrodynamics point of view, the relaxation oscillator, defined on Cantor sets in LC-electric circuit, and its exact solution using the local fractional Laplace transform are obtained. Comparative results among local fractional derivative, Riemann–Liouville fractional derivative and conventional derivative are discussed. Local fractional calculus is proposed as a new tool suitable for the study of a large class of electric circuits.