Can the Doppler be useful for a benchmark analysis of the wave-like properties of memory-dependent telegraphers' equation.

Telegraphers' equation perturbed by a uniformly moving external harmonic impact is investigated to uncover information useful for distinguishing properties of the time evolution patterns that describe either memoryless or memory-dependent modeling of transport phenomena. Memory effects are incorporated into telegraphers' equation by smearing the first- and second-order time derivatives so that the memory kernel smearing the second-order time derivative acts as the smeared derivative of the smeared first-order time derivative. Such a generalized telegraphers' equation (abbreviated as GTE) is solved under initial conditions that specify the values of the solutions and their time derivatives taken at the initial time and boundary conditions that require the sought solutions to vanish either at the x space infinity or the (+l)/(-l) boundaries of a compact domain.