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

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, the$L{T}_{\delta }$-function and $L{C}_{\delta }$-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 $\gamma =\ln 2/\ln 3$ are displayed. As expected, for $\gamma \to 1$, 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.