Noether symmetries and conserved quantities for fractional forced Birkhoffian systems

Abstract

In this paper Noether symmetries and conserved quantities for fractional forced Birkhoffian systems are studied. Firstly, a new fractional Pfaff–Birkhoff variational principle with Riemann–Liouville derivatives and generalized force is established. And from which the fractional forced Birkhoff equations are derived. Secondly, the definitions and the criteria of the invariance of a functional under an ε-parameter group of infinitesimal transformations are given. Finally, the fractional Noether theorems for forced Birkhoffian systems are obtained. And an illustrative example is presented.