Exploring dynamic behaviors of soliton-like pulses in the lossy electrical transmission line model with fractional derivatives: A comparative study

This study aims to explore the intricate behavior of soliton-like pulses within a nonlinear and lossy electrical transmission line. The transmission line is described by a mathematical model called the "beta derivative", which is specifically designed to characterize the propagation of electrical solitons in media with both nonlinearity and dispersion properties. To achieve this goal, the (G '/G(2))-expansion method is applied to a periodically loaded nonlinear beta derivative lossy transmission line with symmetric voltage-dependent capacitances. Soliton-like pulses, including periodic singular, dark, bright, and singular waves, are obtained using the (G '/G(2))-expansion method based on the voltage equation. Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying relevant equations are provided to understand the underlying mechanisms of the soliton family. In terms of fractionality, the profiles of dark or bright waveforms maintain their complete forms, but their smoothness increases as the fractional parameters increase. On the other hand, periodic wave solutions exhibit an increase in periodicity. By adjusting the parameters of the model, the characteristics of the waves can be modified to generate desired wave profiles. Additionally, the study involves a comprehensive comparison among solutions derived from models incorporating the beta, conformable, and M-truncated derivatives. It examines how the amplitude of the solitons is influenced by the fractional parameter, utilizing graphs to visualize this impact by assigning specific fractional parameter values. These pulse-like solitons offer promising potential for integration within telecommunication systems, where they can function as information carriers, facilitating heightened data bit rates. By leveraging the findings of this study, advancements in telecommunication technology can be pursued, leading to enhanced efficiency and improved performance.