The fractal integral operating circuit described by the local fractional derivative

Purpose The purpose of this paper is to derive a new fractal integral operating circuit described by the local fractional derivative. Design/methodology/approach This paper derives a new fractal integral operating circuit described by the local fractional derivative for the first time. On defining the non-differentiable lumped elements through the local fractional derivative, the fractal integral operating circuit is explored detail with the help of the theory of the integrated operational amplifier. Then the fractal integral operating circuit is analyzed by using different input signals on the Cantor sets for different orders χ = 0.4 and χ = ln2/ln3. The fractal integral operating circuit (IOC) becomes the classic IOC for χ = 1 and its corresponding characteristics are also elaborated and compared. Findings It is found that the fractal integral operating circuit becomes the classic integral operating circuit for χ = 1 and its corresponding characteristics are also elaborated and compared. The results of this research can provide some new ideas on the investigation of the fractal models in the circuit systems. Originality/value This paper derives a new fractal integral operating circuit described by the local fractional derivative for the first time. The obtained results reveal that the local fractional derivative is a valid tool to model the fractal circuits and is expected to provide some new ideas to probe and analyze the fractal circuits and systems.