Invariant analysis and conservation laws of (2+1) dimensional time-fractional ZK-BBM equation in gravity water waves

This paper intends to make an in-depth study on the symmetry properties and conservation laws of the (2+1) dimensional time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation with Riemann-Liouville fractional derivative. Symmetry properties have been investigated here via Lie symmetry analysis method. In view of Erdélyi-Kober fractional differential operator, the reduction of (2+1) dimensional time fractional ZK-BBM equation has been done into fractional ordinary differential equation. To analyse the conservation laws, new theorem of conservation law has been proposed here for constructing the new conserved vectors for (2+1) dimensional time fractional ZK-BBM equation with the help of formal Lagrangian.