This paper covers new solitary wave solutions of the fractional Kraenkel-Manna-Merle (KMM) model. The KMM system in its fractional form is studied for the first time. The motion of a nonlinear ultra-short wave pulse through saturated ferromagnetic materials with zero conductivity is depicted in this model. β- derivative is used to study the fractional behavior of the proposed model. Two integration techniques, namely the modified auxiliary equation (MAE) method and generalized projective riccati equations (GPRE) method are efficiently used for extracting of dark, singular and combo solitons along with periodic solutions. The numerical simulations are also carried out by 3D graphs of some of the obtained solutions.

本文介绍了分数阶 Kraenkel-Manna-Merle (KMM) 模型的新孤立波解。首次研究了分数形式的 KMM 系统。该模型描述了非线性超短波脉冲通过具有零电导率的饱和铁磁材料的运动。β - 导数用于研究所提出模型的分数行为。两种积分技术，即修正辅助方程 (MAE) 方法和广义投影 riccati 方程 (GPRE) 方法被有效地用于提取暗孤子、奇异孤子和组合孤子以及周期解。数值模拟也通过一些获得的解决方案的 3D 图形进行。