Fractional Noether's Theorems for El-Nabulsi's Fractional Birkhoffian Systems in Terms of Riemann-Liouville Derivatives

The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional model.The problem of the calculus of variations with fractional derivatives is a hot topic recently.Firstly,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were obtained.Then,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations respectively.Finally,an example is given to illustrate the methods and results appeared in this paper.