Abstract
This research article aims to get superabundant wave solutions of the fractional nonlinear space-time telegraph via two computational schemes (modified Khater (MK) method and simplest equation (SE) method) through a new fractional operator (Atangana-Baleanu [AB] fractional derivative). These solutions are used to calculate the boundary and initial conditions that allow applying the B-spline collection schemes for constructing the numerical solutions and absolute value of error between obtained exact and numerical solutions. On the other hand, the second goal of this research is to investigate the accuracy of used computational schemes and their constructed solutions, where the investigated model is one of the most attractive models for studying in the electrified transmission or electromagnetic waves. This model, which is used to illustrate as the electromagnetic waves do keep mirrored about the wire, or that suspense patterns perform exhibit along the line, describes the cutting-edge or voltage of an electrified transmission range with the day yet distance. Oliver Heaviside formulated this model in 1880.