Abundant soliton solutions on fractional kraenkel manna merle model (FKMM) via new extended of generalized exponential rational function approach (GERFA)

Abstract In this paper, we use the generalized exponential rational function approach (GERFA) for constructing new solitary wave solutions for the fractional Kraenkel Manna Merle (FKMM) model, which is saturated ferromagnetic materials (MF) with a field outside that has very little conductivity, reflects the nonlinear of an ultrashort pulse. The proportional behavior of the suggested model is examined using the beta-derivative (BD). Through the use of this computational method, multiple types of solitons, such as kink, dark, anti-kink, periodic, bright, kink dark, kink bright, anti-kink dark, and anti-kink bright solitons, were obtained for (FKMM). Some of the revealed solutions’ 3D graphs are also employed in the numerical simulations. This investigation demonstrates the efficacy and simplicity of the offered strategy and the simple way to create many new solutions for different kinds of nonlinear partial differential equations, which have significant applications in the engineering and applied sciences. The findings show that the model theoretically has extraordinarily rich soliton structures.