Exact solutions for Kraenkel-Manna-Merle model in saturated ferromagnetic materials using β-derivative

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. beta- 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.