Solitary wave solutions of the fractional Kraenkel-Manna-Merle system via an expansion scheme in physics

Here, using the recently developed extension of the modified rational expansion method (EMREM), we can retrieve the behavior of newly discovered soliton solutions to the fractional Kraenkel-Manna-Merle system (FKMMS). This system represents nonlinear ultrashort pulses in saturated ferromagnetic materials with negligible conductivity in the external field. The fractional efficiency of the proposed method is investigated through the Beta Derivative (BD). As a result, this study highlights the effectiveness and straightforwardness of the offered strategy. Through the application of this computational approach, multiple classes of solitons can be derived like kink shape, bright shape, periodic kink shape, anti-bells shape, bright-dark shape, and singular bells are the results of the applications. The physical characteristics of some reported solutions are illustrated using 3D and 2D projections, along with appropriate parameter values. The results suggest that, theoretically, the model features remarkably intricate soliton structures.