In the present paper, a model of the gravitational waves of water known as the (2 + 1) -dimensional generalized time-fractional (2DGTF) Zakharov Kuznetsov Benjamin Bona Mahony (ZK–BBM) equation is studied. To this end, through employing the Lie symmetry method, exact solutions and reductions are derived for the governing equation. Additionally, classical and nonclassical Lie symmetry generators are acquired, and based on such Lie symmetry generators, conservation laws for the classical and nonclassical vector fields related to the 2DGTF ZK–BBM equation are constructed. Some case studies are given to analyze the impact of the order of the time-fractional derivative on the dynamics of the exact solutions.
