The pulse narrowing nonlinear transmission lines model within the local fractional calculus on the Cantor sets
ISSN: 0332-1649
Article publication date: 11 April 2023
Issue publication date: 23 November 2023
Abstract
Purpose
The fractal and fractional calculus have obtained considerable attention in the electrical and electronic engineering since they can model many complex phenomena that the traditional integer-order calculus cannot. The purpose of this paper is to develop a new fractional pulse narrowing nonlinear transmission lines model within the local fractional calculus for the first time and derive a novel method, namely, the direct mapping method, to seek for the nondifferentiable (ND) exact solutions.
Design/methodology/approach
By defining some special functions via the Mittag–Leffler function on the Cantor sets, a novel approach, namely, the direct mapping method is derived via constructing a group of the nonlinear local fractional ordinary differential equations. With the aid of the direct mapping method, four groups of the ND exact solutions are obtained in just one step. The dynamic behaviors of the ND exact solutions on the Cantor sets are also described through the 3D graphical illustration.
Findings
It is found that the proposed method is simple but effective and can construct four sets of the ND exact solutions in just one step. In addition, one of the ND exact solutions becomes the exact solution of the classic pulse narrowing nonlinear transmission lines model for the special case 9 = 1, which strongly proves the correctness and effectiveness of the method. The ideas in the paper can be used to study the other fractal partial differential equations (PDEs) within the local fractional derivative (LFD) arising in electrical and electronic engineering.
Originality/value
The fractional pulse narrowing nonlinear transmission lines model within the LFD is proposed for the first time in this paper. The proposed method in the work can be used to study the other fractal PDEs arising in electrical and electronic engineering. The findings in this work are expected to shed a light on the study of the fractal PDEs arising in electrical and electronic engineering.
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).
Conflict of interest statement: This work does not have any conflicts of interest.
Citation
Wang, K.-J., Wang, G.-D. and Shi, F. (2023), "The pulse narrowing nonlinear transmission lines model within the local fractional calculus on the Cantor sets", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 42 No. 6, pp. 1576-1593. https://doi.org/10.1108/COMPEL-11-2022-0390
Publisher
:Emerald Publishing Limited
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