Various Closed-Form Solitonic Wave Solutions of Conformable Higher-Dimensional Fokas Model in Fluids and Plasma Physics

This work focuses on finding closed-form analytic solutions of a higher-dimensional fractional model, in conformable sense, known by the (4+1)-dimensional Fokas equation. Fractional partial differential equations (FPDEs) and systems can describe heritable real-world occurrences. However, solving such models can be difficult, especially for nonlinear problems. The homogeneous balancing method (HBM) is investigated and extended to handle the (4+1)-dimensional Fokas equation with Kerr law nonlinearity. The HBM has the ability to solve linear and nonlinear fractional problems, incorporating the concepts of some fractional calculus principles, including fractional derivative techniques. It's important to note that there isn't a single and universally applicable method to solve such equations due to their complexity. The specific form of the equation and the initial or boundary conditions influence the solution method chosen. The results obtained from the extended HBM are compared to those in the literature to prove the strategy's efficacy. This paper proposes expanding the HB technique with result analysis to solve nonlinear FPDEs, demonstrating its feasibility and efficiency