ABSTRACT
In this chapter, some recent analytical schemes are employed to construct novel computational solutions of the fractional quantum version of the relativistic energy--momentum relation that is mathematically represented by the nonlinear fractional Klein–Gordon equation. This model describes the spinless relativistic composite particles, like the pion. This process uses a new fractional definition (Atangana–Baleanu derivative operator), which converts the fractional form of the equation to integer-order nonlinear equation; then, by using the obtained analytical solutions to evaluate the initial and boundary conditions, some numerical solutions are discussed. Moreover, the stability property of the obtained solutions is tested to show the ability of our obtained solutions use in physical experiments. The novelty and advantage of the proposed methods are illustrated by applying this model. Some sketches are plotted to show more about the dynamical behavior of this model.
