Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations

Abstract

Abstract Fractional nonlinear evolution equations concerning conformable fractional derivative are effective models to interpret intricate physical phenomena in the real world. The space-time fractional foam drainage equation and the coupled mKdV equations with conformable fractional derivative are important model equations for shallow water waves, the waves of flow of liquid between bubbles, the capillary waves, the waves of foam density, the electro-hydro-dynamical model, the ion acoustic plasma waves etc. In this study, we extract the functional and further general exact wave solutions comprising the rational, trigonometric, exponential and hyperbolic functions to the above stated models taking the advantage of the auxiliary equation method with the assistance of the fractional complex transformation. The method is convenient, reliable and delivers fresh and useful solutions to fractional differential equations ascend in physical and engineering sciences. We depict figures of the obtained solutions in order to illustrate the inner structure associated to the phenomena.