Solitary waves of M-fractional low-pass nonlinear electrical transmission line model arising in network system

In this study, we analyze the solitary wave behavior of a truncated M-fractional low-pass nonlinear electrical transmission line (NLETLs) model. NLETL models are relevant to computer network systems, particularly for high-speed data transmissions. They influence the behavior of signals traveling through network cables. To investigate the dynamics of solitary waves in the model, we applied the modified Sardar sub-equation and extended the sinh-Gordon equation expansion methods. We illustrated the 2D, 3D, and contour shapes of selected solutions for appropriate values of the NLETLs dynamics using Mathematica-14. Kink, anti-kink, bright-dark bell, dark bell, M-shaped periodic soliton, and logarithmic wave solutions were obtained. The results indicate that the proposed techniques may provide valuable, powerful, and efficient insights into the dynamics of nonlinear evolution models. The role of the fractional order derivative in making optical solutions is investigated in detail, which opens up opportunities for the creation of more complex models that can more accurately simulate optical phenomena in the real world.