The (2+1)-dimensional generalized fifth-order KdV equation in its time-fractional form: Lie point symmetries, exact solutions and conservation laws

KdV-type equations play an important role in many fields. In this paper, we focus on the (2+1)-dimensional generalized fifth-order KdV equation. Firstly, based on the semi-inverse method and fractional variational theory, we formulate its time-fractional form in the sense of the Riemann–Liouville fractional derivative. Next, we employ the Lie point symmetry method to derive Lie point symmetries of the fractional equation, which admits a systematic reduction of the studied equation into a hierarchy of reduced equations in fewer dimensions. The exact solutions are then obtained, and the convergence analysis is performed. Finally, the nontrivial conservation laws for the obtained Lie point symmetries are constructed using the conservation theorem and generalization of Noether operators.