The present study focuses on the acquisition of traveling wave solutions associated with the conformable time-fractional Zoomeron equation through the utilization of the modified exponential function method (MEFM). The solution functions derived from mathematical computations encompass hyperbolic, trigonometric, and rational functions. Various graphical representations, such as 2D, 3D, contour graphs, and density graphs, are utilized to visually depict the distinct features of the solution functions derived from the determination of suitable parameters.