Analytical and numerical solutions for the current and voltage model on an electrical transmission line with time and distance

This research paper employs three different techniques on the fractional nonlinear space-time telegraph equation to get the solitary traveling wave solutions, semi-analytical wave solution, and numerical solutions. We implement a modified Khater method, Adomian decomposition method, and B-spline techniques (cubic, quantic, and septic) on the fractional telegraph equation. This model is one of the fundamental equations in an electrical transmission and electromagnetic waves that describes the current and voltage on an electrical transmission line with time and distance. It derived by Oliver Heaviside in the 1880s and used to discuss the mirror phenomena of the electromagnetic waves and wave patterns through along line. New structure forms of solitary traveling wave solutions are obtained, and the comparison between the three kinds of solutions is given. The obtained solutions verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows the power and effectiveness of them for applying to many different forms of the nonlinear partial differential equation with integer order and fractional order.