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.

Keywords

• fractional derivatives
• symmetry
• fractional variational calculus
• fractional euler–lagrange equations
• conservation laws
• noether’s theorem