Solitary wave solutions for the conformable time-fractional coupled Konno-Oono model via applications of three mathematical methods

This research extensively investigates the solitary wave solutions of the fractional coupled Konno–Oono model, a prevalent framework in diverse scientific and engineering disciplines. Three mathematical methods called the simple equation method, the modified extended auxiliary equation mapping method, and the exponential-expansion method are gradually employed to derive the analytical solutions. Moreover, Mathematica 13.0 software is used to perform the analytical computations and graphical simulations. The explored outcomes have significant applications in the realm of magnetic fields. After the careful selection of parametric values under constrained conditions, some solutions are plotted in 2-dimensional and 3-dimensional spaces to understand the physical phenomena of the concerned model. Importantly, our findings affirm that the employed methods not only yield complete and uniform responses but also showcase simplicity, effectiveness, and remarkable computational efficiency. Hence, our research contributes valuable insights into the behavior of the fractional coupled Konno–Oono model, paving the way for enhanced comprehension and potential applications in magnetic field studies.