On a fractal LC-electric circuit modeled by local fractional calculus

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.