Fractional variational symmetries of Lagrangians, the fractional Galilean transformation and the modified Schrodinger equation

We develop the fractional variational symmetries of a Lagrangian for dynamical systems with finite number degrees of freedom. Our approach is based on the fractional actionlike variational approach where we report the Lagrangian formalism where constants of motion are obtained. It was observed that a fractional version of the Galilean transformation may be derived which when applied to the Schrodinger equation revealed some interesting consequences.