<p>In this study, we investigate wave solutions to the space–time fractional (1 + 1)-dimensional Sawada-Kotera equation, a nonlinear integrable evolution equation with noteworthy applications in shallow water waves and other fluid systems utilizing the extended modified auxiliary equation mapping method, an adaptable and specific analytical technique. We establish several novel solitary wave solutions, including trigonometric, rational, exponential, and hybrid solitary wave solutions to the stated model under two different sets of parameters. The solutions include a variety of waveforms such as kink, pulse, general, and other solitons, which hold numerous applications in nonlinear physics and engineering. We examine the effects of the beta fractional parameter on the obtained solitons analytically and graphically. The stability of these solutions under system parameters is also assessed. Graphical representations of the solutions are provided in 2D, contour, and 3D formats using MATLAB with appropriately selected parameter values. The method proves to be effective and efficient for explaining the fractional nonlinear model, demonstrating its potential for addressing the space–time fractional Sawada-Kotera equation.</p>