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

Kang-Jia Wang (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo, China)
Jing-Hua Liu (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo, China)

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering

ISSN: 0332-1649

Article publication date: 12 May 2023

Issue publication date: 23 November 2023

55

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 -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 -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 -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 -order R-C ZSRC on the Cantor sets are analyzed and presented through the 2-D curves. It is found that the -order R-C ZSRC becomes the classic one when = 1. The comparative results between the -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 -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.

Keywords

Acknowledgements

This work is supported by the Key Programs of Universities in Henan Province of China (22A140006), the Fundamental Research Funds for the Universities of Henan Province (NSFRF210324), Program of Henan Polytechnic University (B2018-40), the Innovative Scientists and Technicians Team of Henan Provincial High Education (21IRTSTHN016).

Declaration of interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.

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

Publisher

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Emerald Publishing Limited

Copyright © 2023, Emerald Publishing Limited

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