Invariance analysis and some new exact analytic solutions of the time-fractional coupled Drinfeld-Sokolov-Wilson equations

In this work, the fractional Lie symmetry method is used to find exact solutions of time-fractional coupled Drinfeld-Sokolov-Wilson equations with Riemann-Liouville derivative. Time-fractional are obtained by replacing first-order time derivative derivatives (FD) order $\alpha$ in classical (DSW) model. Using method, generators obtained. With help generators, FCDSW reduced into ordinary differential (FODEs) Erd$\acute{e}$lyi-Kober operator. Also, we have solution and shown effects non-integer value on graphically. The effect behavior studied Finally, new conservation laws constructed along formal Lagrangian generalization Noether operators. It quite interesting analytic explicit form.