Symmetry classification and exact solutions of (3 + 1)-dimensional fractional nonlinear incompressible non-hydrostatic coupled Boussinesq equations

Abstract

The symmetry classifications of two fractional higher dimensional nonlinear systems, namely, (3 + 1)-dimensional incompressible non-hydrostatic Boussinesq equations and (3 + 1)-dimensional Boussinesq equations with viscosity, are discussed. Both the fractional Boussinesq equations are considered to have derivatives with respect to all variables of fractional type, and some exact solutions are reported along with graphical illustrations.