Fractional low-pass electrical transmission line model: Dynamic behaviors of exact solutions with the impact of fractionality and free parameters

Abstract

In this study, we focus on extracting soliton solutions to the differential equation of fractional order governing wave propagation in low-pass electrical transmission lines by the (G'/G2)-expansion method. By a simple linear fractional transformation, we convert the model equation to an ordinary differential equation. Thereupon, through the use of the (G'/G2)-expansion method, various types of solitary wave solutions to the equation of interest are achieved. All the received solutions are verified using Maple software. To show the dynamical behavior of some of the acquired solutions representing singular-periodic, singular, anti-kink, periodic, and bright soliton solutions, their two and three-dimensional profiles are displayed by selecting suitable values of the solutions’ free parameters. Impacts of the fractionality and free parameters on the dynamical behavior of the attained soliton solutions are presented graphically and discussed elaborately. A comparison of our explored solutions with those obtained in the literature is also made. The comparison, wherever available, shows no noticeable difference between our attained results and the published ones. The results that came out through this investigation expose the productivity and powerfulness of the adoptive method for excerpting a diversity of wave solutions to nonlinear evolution equations arising in the fields of mathematics, engineering, and physics.