Lie Symmetry Analysis and Exact Solutions of Conformable Generalized Fractional Partial Differential Equations

In this work, we investigate the invariance properties of nonlinear fractional partial differential equations (NLFPDEs) involving conformable fractional derivatives in both spatial and temporal variables by employing the framework of Lie symmetry analysis. Specifically, the study focuses on the generalized modified Burgers equation and the generalized modified Kortewegde Vries (mKdV) equation with conformable fractional derivatives. The corresponding infinitesimal generators and symmetry vector fields for both the models are systematically derived. Then by using these Lie symmetries, the governing equations are transformed into ordinary differential equations. To obtain exact analytical solutions, the ansatz methods and the (F/G)-expansion technique is applied on the reduced equations. Furthermore, the generalized mKdV equation is transformed into an autonomous dynamical system, enabling a qualitative investigation through bifurcation theory.