Pattern Formation of a Bubbly Fluid Mixture under the Effect of Thermodynamics via Kudryashov-Sinelshchikov Model

In this paper, new explicit wave solutions via liquid-gas bubbles are obtained for the fractional Kudryashov-Sinelshchikov (KS) equation under thermodynamic assumptions. A new fractional definition is applied to get these solutions that are utilized to represent the phenomenon of pressure waves under thermodynamic conditions. Two analytical techniques are used to explore the model which is sinh-Gorden equation expansion and Riccati-Bernoulli Sub-ODE methods. These approaches provide complex hyperbolic, hyperbolic, complex trigonometric, and trigonometric solutions for the fractional KS equation, particularly singular, combined singular, dark, bright, combined dark-bright, and other soliton solutions. Furthermore, acquired results are illustrated by 3D graphs for suitable parametric values that highlight the physical importance and dynamical behaviors of the equation. It is also demonstrated that the purposed approaches are powerful strategies for developing exact traveling wave solutions for a wide range of problems found in mathematical sciences.