Analysis of the(3+1)-Dimensional Fractional Kadomtsev–Petviashvili–Boussinesq Equation: Solitary, Bright, Singular, and Dark Solitons

We looked at the (3+1)-dimensional fractional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which comes up in fluid dynamics, plasma physics, physics, and superfluids, as well as when connecting the optical model and hydrodynamic domains. Furthermore, unlike the Kadomtsev–Petviashvili equation (KPE), which permits the modeling of waves traveling in both directions, the zero-mass assumption, which is required for many scientific applications, is not required by the KP-B equation. In several applications in engineering and physics, taking these features into account allows researchers to acquire more precise conclusions, particularly in studies pertaining to the dynamics of water waves. The foremost purpose of this manuscript is to establish diverse solutions in the form of exponential, trigonometric, hyperbolic, and rational functions of the (3+1)-dimensional fractional (KP-B) via the application of four analytical methods. This KP-B model has fruitful applications in fluid dynamics and plasma physics. Additionally, in order to better explain the potential and physical behavior of the equation, the relevant models of the findings are visually indicated, and 2-dimensional (2D) and 3-dimensional (3D) graphics are drawn.