Analysis of Lie symmetries with conservation laws for the (3+1) dimensional time-fractional mKdV–ZK equation in ion-acoustic waves

In this paper, symmetry properties and conservation laws of the (3+1) dimensional time-fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation have been studied with Riemann–Liouville fractional derivative. Fractional Lie symmetry method has been used here for getting symmetry properties of (3+1) dimensional time-fractional mKdV–ZK equation. Here, the reduction of (3+1) dimensional time-fractional mKdV–ZK equation into fractional ordinary differential equation has been done by using Erdélyi–Kober fractional differential operator. Also, by using the new conservation theorem, the new conserved vectors for (3+1) dimensional time-fractional mKdV–ZK equation have been constructed with the help of formal Lagrangian with a detail derivation.