Exact Solution of the Time Fractional Variant Boussinesq-Burgers Equations

In the present article, we consider a nonlinear time fractional system of variant Boussinesq-Burgers equations. Using Lie group analysis, we derive the infinitesimal groups of transformations containing some arbitrary constants. Next, we obtain the system of optimal algebras for the symmetry group of transformations. Afterward, we consider one of the optimal algebras and construct similarity variables, which reduces the given system of fractional partial differential equations (FPDEs) to fractional ordinary differential equations (FODEs). Further, under the invariance condition we construct the exact solution and the physical significance of the solution is investigated graphically. Finally, we study the conservation law of the system of equations.