Generalization of Mei symmetry approach to fractional Birkhoffian mechanics

Abstract

The fractional Birkhoffian systems are investigated for Mei symmetry and corresponding conserved quantities. It is divided into two cases, one is standard fractional Birkhoffian systems, the other is fractional Birkhoffian systems under quasi-fractional dynamics models of El-Nabulsi type. The fractional Pfaff-Birkhoff principles are presented, and Birkhoff’s equations are deduced. Mei symmetry and its determining equations are established. Mei symmetry theorems are proved and fractional conserved quantities are obtained.