On the zero state-response of the ℑ-order R-C circuit within the local fractional calculus

Abstract

Purpose

As a powerful mathematical analysis tool, the local fractional calculus has attracted wide attention in the field of fractal circuits. The purpose of this paper is to derive a new ℑ-order non-differentiable (ND) R-C zero state-response circuit (ZSRC) by using the local fractional derivative on the Cantor set for the first time.

Design/methodology/approach

A new ℑ-order ND R-C ZSRC within the local fractional derivative on the Cantor set is derived for the first time in this work. By defining the ND lumped elements via the local fractional derivative, the ℑ-order Kirchhoff voltage laws equation is established, and the corresponding solutions in the form of the Mittag-Leffler decay defined on the Cantor sets are derived by applying the local fractional Laplace transform and inverse local fractional Laplace transform.

Findings

The characteristics of the ℑ-order R-C ZSRC on the Cantor sets are analyzed and presented through the 2-D curves. It is found that the ℑ-order R-C ZSRC becomes the classic one when ℑ = 1. The comparative results between the ℑ-order R-C ZSRC and the classic one show that the proposed method is correct and effective and is expected to shed light on the theory study of the fractal electrical systems.

Originality/value

To the best of the authors’ knowledge, this paper, for the first time ever, proposes the ℑ-order ND R-C ZSRC within the local fractional derivative on the Cantor sets. The results of this paper are expected to give some new enlightenment to the development of the fractal circuits.

Citation

Wang, K.-J. and Liu, J.-H. (2023), "On the zero state-response of the ℑ-order R-C circuit within the local fractional calculus", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 42 No. 6, pp. 1641-1653. https://doi.org/10.1108/COMPEL-11-2022-0380