An effective computational approach to the local fractional low-pass electrical transmission lines model

• Published in: Alexandria engineering journal Vol. 110; pp. 629 - 635
• Main Author: Wang, Kang-Jia
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2025; Elsevier
• Subjects: Auxiliary function; Cantor sets; Local fractional derivative; Low-pass electrical transmission lines model; Mittag-Leffler function; Cantor sets; Local fractional derivative; Low-pass electrical transmission lines model; Mittag-Leffler function; Auxiliary function
• ISSN: 1110-0168
• DOI: 10.1016/j.aej.2024.07.021

In this research, a new fractional low-pass electrical transmission lines model (LPETLM) described by the local fractional derivative (LFD) is derived for the first time. By defining the Mittag-Leffler function (MLF) on the Cantor set (CS), two special functions, namely, theLTδ-function and LCδ-function, are extracted to develop an auxiliary function, which is employed to look for the non-differentiable (ND) exact solutions (ESs) together with Yang’s non-differentiable transformation. Eight sets of the ESs are obtained and the corresponding dynamic performances on the CS for γ=ln2/ln3 are displayed. As expected, for γ→1, the ESs of the local fractional LPETLM become the ESs of the classic LPETLM and the outlines are also depicted graphically. The outcomes confirm that our new method is a promising tool to handle the local fractional PDEs in the electrical and electronic engineering.