Abundant dynamical solitary waves through Kelvin-Voigt fluid via the truncated M-fractional Oskolkov model

Abstract

This effort explores the dynamic behavior of solitary wave fronts using the Oskolkov model in a truncated M-fractional derivative form. This effort has been performed through the application of modified extended tanh and a novel form of modified Kudryashov techniques. All obtained solutions manifest in the form of sinusoidal, hyperbolic, and constant basis function solutions within the fractional model. Within this framework, the applied techniques yield various solitary wave structures, including bright and dark bell solitons, kinks, anti-kinks, linked lumps, and collisions of kinks. Additionally, they produce singular kink solitons and lump waves. The effects of fractionality and the coefficient of the highest-order derivative are depicted in Figs. 1 through 11. Moreover, all figures are organized to illustrate the properties of the innovative soliton wave propagations. The studies have also revealed that the fractional Oskolkov model can support both fundamental and higher-order solitons, each characterized by distinct properties and highly efficient behaviors. Various dynamical solitary waves obtained here can be described transmission waves through Kelvin-Voigt fluid with real happenings as it represented by fractional form.