Abstract:
The symmetry and conserved quantity for fractional generalized Birkhoffian systems are studied. Firstly, the fractional generalized Birkhoff’s equations are established according to the fractional generalized Pfaff-Birkhoff principle. Secondly, the definition and the determining equation of Mei symmetry of fractional Birkhoffian system are established based on the fact that the dynamics function in the dynamics equation still satisfies the invarianceof the original equation after undergoing infinitesimal transformation of the group. Thirdly, Mei symmetry theorems of the system are given and proved, and fractional Mei conserved quantity is obtained. The Mei symmetry theorems of integer order generalized Birkhoffian system, fractional Birkhoffian system and fractional Hamiltonian system are special cases. Finally, an example is given to illustrate the application of the theorems.