The article explores the conformable nonlinear Wazwaz-Kaur-Boussinesq equation in \((3+1)\) -dimensions. It begins by presenting fundamental definitions and characteristics of the conformable derivative. Subsequently, the modified generalized exponential rational function method with two different structures is employed to derive exact solutions to the problem. The results are illustrated through some 3D, 2D, and contour plots of some of the obtained solutions. In addition, sensitivity and bifurcation analysis are conducted, and some related plots have been included. These solutions highlight the potential applications of the studied model in physical sciences to address real-world scenarios. The method demonstrates its ability to solve a wide range of fractional differential equations with significant results.
