Dynamics of traveling waves of variable order hyperbolic Liouville equation: Regulation and control

Abstract

Traveling waves remain significant in Applied Sciences mostly because they involve the movement of energy carrier particles. In this paper, traveling waves described by a generalized system, the fractional variable order hyperbolic Liouville model is solved numerically by means of Crank-Nicholson scheme. Detailed analysis are performed and prove that the numerical method is stable and converges. Simulations reveal that the model's variable order derivative (a function of time and position variables) has a considerable impact on the dynamics of the whole system. It influences the movement and the shape of the resulting waves including their amplitude, their wavelength as well as their compression and rarefaction processes. Such a variable order derivative becomes, due to these results, a substantial parameter and non-constant tool for the regulation and control of models describing wave motion.