Fractional derivative generalization of Noether's theorem

Abstract

The symmetry of the Bagley-Torvik equation is investigated by using the Lie group analysis method. The Bagley-Torvik equation in the sense of the Riemann-Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples are presented as an application of the theory.