New Solitons and Multishock Wave Structures for the Conformable Space Fractional Burger and Time Fractional Sharma-Tasso-Olver Models

Abstract

This present paper studies the conformable space fractional Burgers, and the time fractional Sharma-Tasso-Olver models; both are highly important for nonlinear diffusive waves in fluid dynamics, sound waves in a viscous medium, and flow in field soils, as well as in gas and plasma dynamics. To retrieve explicit solutions of the fractional differential models, we propose an integral scheme, namely, Modified Kudryashov method. We obtain periodic, solitary, mixed periodic-soliton, and polynomial solutions through the approach. In particular, we exhibit topological kink-dark bell wave, topological kink, singular kink, bright bell, peakon solitons, and periodic shape waves to apply suitable values on parameters for both distinct models. The impact of fractionality on the wave shape and its deformation is analyzed and discussed graphically. We also investigate multishock wave’s solutions of both models and analyzed the effect of each existing parameters involved in the obtained solutions. To visualize the real characters of the solitary solutions, the graphical elucidation in 3D and 2D profiles are plotted. In computational effort and realization, it is emphasized that the proposed scheme is friendly useful, highly effective, and a powerful mathematical tool to extract exact solitary wave solutions for the differential models, as well as fractional differential models.