In this work, we investigate invariance analysis, conservation laws, and exact power series solutions of time fractional generalized Drinfeld–Sokolov systems (GDSS) using Lie group analysis. Using Lie point symmetries and the Erdelyi–Kober (EK) fractional differential operator, the time fractional GDSS equation is reduced to a nonlinear ordinary differential equation (ODE) of fractional order. Moreover, we have constructed conservation laws for time fractional GDSS and obtained explicit power series solutions of the reduced nonlinear ODEs that converge. Lastly, some figures are presented for explicit solutions.

In this work, one-point Lie symmetry method is applied to time fractional super KdV equation in order to obtain similarity variables and similarity transformations with Riemann–Liouville derivative. These transformations reduce the governing equation to an ordinary differential equation of fractional order. A new and effective conservation theorem based on Noether’s theorem is used to obtain conserved vectors. Then, we construct power series solutions for the reduced time fractional ordinary differential equation and prove that the solutions are convergent. Lastly, some interesting graphs are given to explain physical behaviors.

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