In this paper, the problem of constructing the Lie point symmetries group of the nonlinear partial differential equation appeared in mathematical physics known as the generalized KdV-Like equation is discussed. By using the Lie symmetry method for the generalized KdV-Like equation, the point symmetry operators are constructed and are used to reduce the equation to another fractional ordinary differential equation based on Erdélyi-Kober differential operator. The symmetries of this equation are also used to construct the conservation Laws by applying the new conservation theorem introduced by Ibragimov. Furthermore, another type of solutions is given by means of power series method and the convergence of the solutions is provided; also, some graphics of solutions are plotted in 3D.

In this paper, Lie symmetries of time-fractional KdV-Like equation with Riemann-Liouville derivative are performed. With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. Finally, Ibragimov’s theorem has been employed to construct the conservation laws.