A comprehensive study of wave dynamics in the (4+1)-dimensional space-time fractional Fokas model arising in physical sciences

The higher dimensional Fokas equation is the integrable expansion of the Davey–Stewartson and Kadomtsev–Petviashvili equations. In wave theory, the Fokas model plays a crucial role in explaining the physical phenomena of waves both inside and outside of water. The (4+1)-dimensional fractional-order Fokas equation is the subject of this article. Two effective approaches are employed to obtain the solutions for the considered equation: the generalized auxiliary equation technique and the G^′/(bG^′+G+a) technique. Several novel soliton solutions are obtained, including periodic solitary waves, bright solitons, and dark solitons. Various parametric values are employed to produce these new soliton waves at certain fractional order levels α. Furthermore, the bilinear version of the equation helps to develop its two-wave, three-wave, and multi-wave, as well as lump and rogue wave solutions. The properties of the solutions to the underlying problem are most effectively analyzed through the use of graphical representations. These outcomes and techniques can be used to study various fractional-order problems that emerge in wave theory, such as those in physics, hydraulics, optical technology, quantum mechanics, and plasma particles.