Abstract:
Based on the fractional integral extended by exponential law, Noether symmetries and conserved quantities of quasi−fractional Birkhoffian systems in event space have been studied. Firstly, based on the definition of fractional integral extended by exponential law, the quasi−fractional Pfaff action in event space is presented, the quasi−fractional Pfaff−Birkhoff principle in event space is established, and the Pfaff−Birkhoff−d'Alembert principle is derived, and the differential equations of motion for quasi−fractional Birkhoffian systems in event space are obtained. Secondly, the total variation of Pfaff action is calculated, and two variational formulas of quasi−fractional Pfaff action in event space are given. The definition and criterion of Noether symmetry of quasi−fractional Birkhoffian system in event space are established. Finally, Noether’s theorems for quasi−fractional Birkhoffian systems in event space are established which reveal the internal relationship between Noether symmetries and conserved quantities. If the fractional time integral parameter
\gamma = 1
, the theorems degrade to Noether’s theorems of classical Birkhoffian systems in event space. At the end of the paper, an example is given to illustrate the application of the results.