Exploring Exact Travelling Wave Solutions of Space–Time Fractional Higher‐Dimensional Evolution Equations in Plasma Physics

ABSTRACT In this work, we investigate the exact travelling wave solutions of the space–time fractional (3 + 1)‐dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (KdV‐CBS) equation and the negative‐order (3 + 1)‐dimensional KdV‐CBS equation (nKdV‐nCBS) by utilizing Sub equation method (SEM). The fractional partial differential equations (FPDEs) are transformed to nonlinear ordinary differential equations (ODEs) by using a suitable traveling wave transformation. Numerous soliton‐type solutions, such as kink, anti‐kink, singular, singular periodic, and multi‐soliton singular wave forms, are generated using the suggested approach. Both two and three‐dimensional graphical representations are used for understanding the behavior of these acquired solutions followed by physical significance. The obtained solutions are indeed beneficial for analyzing the wave propagation in complex media like nonlinear optics, hydrodynamics, plasmas, and fluid systems. The SEM provides a simple, effective, and efficient method for solving high‐dimensional nonlinear FPDEs in contrast to other approaches in the literature. The results presented in this work not only enrich the family of exact solutions for fractional KdV‐type models but also demonstrate the effectiveness of the conformable derivative framework in capturing complex nonlinear wave dynamics relevant to mathematical physics.