On Lie Symmetry Analysis and Analytical Solutions of the Time-Fractional Modified ZKB Equation in Mathematical Physics
In this article, we explore the time-fractional modified Zakharov-Kuznetsov-Burgers (MZKB) equation of (3+1) dimensions. The Lie symmetry analysis is used to identify the symmetries and vector fields for the equation understudy with the assistance of the Riemann-Liouville derivatives. These symmetries are then employed to build a transformation that reduces the above equation into a nonlinear ordinary differential equation of fractional order with the aiding of ErdLélyi-Kober fractional operator. Further, two sets of new analytical solutions are constructed by the fractional sub-equation method and the extended Kudryashov method. Subsequently, we graphically represent these results in the 2D and 3D plots with physical interpretation for the behavior of the obtained solutions. The conservation laws that associate with the symmetries of the equation are also constructed by considering the new conservation theorem and the formal Lagrangian L. As a final result, we anticipate that this study will assist in the discovery of alternative evolutionary processes for the considered equation
