The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative

Abstract

Local fractional calculus has gained wide attention in the field of circuit design. In this paper, we propose the zero-input response(ZIR) of fractal RC circuit modeled by local fractional derivative(LFD) for the first time. With help of the law of switch and the Kirchhoff Voltage Laws, the transient local fractional ordinary differential equation is established, and the corresponding exact solution behavior defined on Cantor sets is presented. What we found especially interesting was that the fractal RC becomes the ordinary one in the particular case κ = 1. The results obtained in this paper reveal that the local fractional calculus is a powerful tool to analyze the fractal circuit systems.

Keywords

• Local fractional calculus
• Local fractional derivative
• Zero-input response
• Fractal circuit systems