Traveling Wave Analysis for the Fractional ZK-MEW Equation via Exp-Function Method

In this study, we investigate the fractional Zakharov–Kuznetsov–modified equal width (ZK-MEW) equation, which arises in modeling nonlinear wave propagation in dispersive media such as plasma physics and nonlinear optics. While classical studies have primarily focused on integer-order models, the incorporation of fractional derivatives allows for the inclusion of memory and hereditary effects, leading to more realistic physical descriptions. An improved Exp-function method is employed to derive new exact traveling wave solutions of the considered fractional model. The governing fractional partial differential equation is transformed into a nonlinear ordinary differential equation via an appropriate traveling wave transformation. The resulting system is solved analytically to obtain multiple classes of solutions, including lump, soliton, compacton, and peakon structures. Compared to existing analytical approaches, the proposed method provides a systematic and efficient framework for constructing diverse wave solutions in fractional higher-dimensional systems. The influence of the fractional parameter on wave dynamics is examined through graphical analysis, revealing its significant role in controlling amplitude, localization, and propagation speed. The novelty of this work lies in the application of an improved Exp-function method to a fractional higher-dimensional ZK-MEW equation and the explicit construction of multiple physically meaningful wave structures. These findings contribute to the growing body of research on fractional nonlinear systems and provide a foundation for further analytical and numerical investigations.