Abundant wave solutions of conformable space-time fractional order Fokas wave model arising in physical sciences

The higher dimensional Fokas equation is the integrable expansion of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations. The Fokas model has an important role in wave theory, to describe the physical phenomena of waves on the surface and inside the water. This article deals with the (4+1)-dimensional conformable space-time fractional-order Fokas partial differential equation. Two efficient methods, namely the generalized exp(-ϕ(ξ))-expansion and improved F-expansion methods, are formulated for conformable fractional-order partial differential equation and new wave structures of fractional order Fokas model are constructed. The different kinds of new solitons are achieved such as bright soliton, dark soliton, Kink and anti-kink solitons, periodic solitary waves, and traveling waves. These new soliton waves are constructed at some values of fractional order α and using different parametric values of the methods by using the software package Mathematica. Newly obtained soliton solutions are compared with the available soliton solutions with different fractional derivatives in the literature. Some of the achieved results are explained 2D and 3D graphically. The new results interpreting that these obtained solutions can be a part, to complete the family of solutions and considered methods are effective, simple, and easy to use. Furthermore, this paper gives an idea, how can reduce the conformable fractional order higher dimensional partial differential equation into an ODE of one variable to obtain the exact solutions. These results and methods can be help to investigate the other higher-dimensional conformable fractional-order models which appear in nonlinear wave theory such as optics, quantum gases, hydrodynamics, photonics, plasmas, and solid-state physics.