New exact wave solutions to the space-time fractional-coupled Burgers equations and the space-time fractional foam drainage equation

Abstract

Abstract The space-time fractional-coupled Burgers equations and the space-time fractional foam drainage equation are important as an electro-hydro-dynamical model to progress the local electric field and ion acoustic waves in plasma, the shallow water wave problems, and also fluid flow of liquid through foam arisen by gravity and capillarity. In this article, we determine new and further general exact wave solutions to the above-mentioned space-time fractional equations using the generalized (G′/G)-expansion method with the assistance of the fractional complex transformation. It is shown that the method is further effective, convenient, and can be used to establish new solutions for other kind non-linear fractional differential equations arising in mathematical physics. Finally, we depict the 3D and 2D figures of the obtained wave solutions in order to interpret them in geometrical sense.