<p>Anyone involved in coastal and ocean engineering must have a thorough understanding of the interactions between waves and nonlinear media, fluid flows in dynamic systems, and wave propagation in shallow water. The fractional Allen equation provides a fundamental explanation for these phenomena. Understanding fluid flow in dynamic systems, how waves propagate in shallow water, and how waves interact with nonlinear media are essential for anybody working in coastal and ocean engineering. Essentially, these events are modelled by the fractional Allen equation. This was resolved by creating unique closed-form solutions utilising conformable derivatives and the fractional differential transform to solve the fractional Allen equation in space-time. The soliton wave morphologies, such as bell, kink, multiple kink, singular kink, and periodic waves, are produced by the procedure. It is well recognised that there are a lot of unknowns in this equation. We presented our findings, and of more understandable physical explanation was given by 3D, contour, and density graphs produced using mathematical tools such as Maple. I present reliable, consistent, and useful results for the propagation of nonlinear waves using our technique. This work enhances the subject of ocean and coastal engineering and broadens our understanding of wave behaviour in complicated systems.</p>