Abundant dynamical solitary waves solutions of M -fractional Oskolkov model

Abstract

This work uses a truncated M-fractional derivative variant of the Oskolkov model to investigate the dynamic behavior of solitary wavefronts. The methods used in this framework produce a variety of solitary waveforms, such as bright and dark solitons. A suitable choice of the free parameters is used to investigate the geometrical structures for the wave solutions, which are further characterized by stable bright periodic and soliton waves. The coefficient of the highest-order derivative and the effects of fractionality are shown in the figures. Moreover, the graphics are arranged to highlight the characteristics of novel soliton wave propagation. The findings of this research demonstrate that the fractional Oskolkov model may accommodate fundamental and higher-order soliton behaviors, each of which has unique characteristics. The fractional form of the several dynamical solitary waves seen in the study represents their practical ramifications. These waves can be seen as transmission waves via a Kelvin-Voigt fluid.