The plethora of explicit solutions of the fractional KS equation through liquid–gas bubbles mix under the thermodynamic conditions via Atangana–Baleanu derivative operator

Abstract

Abstract Novel explicit wave solutions are constructed for the Kudryashov–Sinelshchikov (KS) equation through liquid–gas bubbles mix under the thermodynamic conditions. A new fractional definition (Atangana–Baleanu derivative operator) is employed through the modified Khater method to get new wave solutions in distinct types of this model that is used to describe the phenomena of pressure waves through liquid–gas bubbles mix under the thermodynamic conditions. The stability property of the obtained solutions is tested to show the ability of our obtained solutions through the physical experiments. The novelty and advantage of the proposed method are illustrated by applying to this model. Some sketches are plotted to show more about the dynamical behavior of this model.

Keywords

• Fractional nonlinear Kudryashov–Sinelshchikov (KS) equation
• ABR $\mathcal{ABR}$ fractional operator
• Modified Khater (mK) method
• Stability property