Abstract
This study analyzes the exact solutions of the compliance fractional non-linear time-space telegraph (FNLTST) equation by Oliver Heaviside in 1880 via three non-applied analytical schemes. The solutions obtained to define the advanced or voltage spectrum of electrified transmission with day-to-day distance from electrical communication or the application of electromagnetic waves. Many new solutions are obtained, and three distinct styles of drawings are introduced (two-dimensional, three-dimensional, and density plots). Furthermore, stability characterization of the solutions is addressed using the properties of the Hamiltonian system. The originality of this study is shown by matching the solutions built with solutions produced previously using various analytical methods. Overall, the success of the three systems demonstrates their quality, intensity, and capacity to cope with several different types of non-linear evolutionary equations.