Noether symmetry theory of fractional order constrained Hamiltonian systems based on a fractional factor

In this paper, we study the Noether Symmetries and conserved quantities of fractional order constrained Hamiltonion systems based on a fractional factor. Firstly, we put forward the calculation method of fractional derivative by the fractional factor, and give the variational problem of fractional systems; Secondly, according to the regular action quantity under the infinitesimal transformation for invariance, we give the definition of Noether symmetric transformation and the criterion equation; Further, according to the relation between symmetries and conserved quantities, we obtain the Noether theorem and its inverse problem. Finally, an example is given to illustrate the application of the result. The research shows that it keeps natural height consistency in the form with the classical integer order constrained mechanical systems by using the derivative definition with fractional factor, the fractional factor can establish the connection between the fractional order systems and the integer order systems.