Conserved Quantities for Constrained Hamiltonian System within Combined Fractional Derivatives

Singular systems, which can be applied to gauge field theory, condensed matter theory, quantum field theory of anyons, and so on, are important dynamic systems to study. The fractional order model can describe the mechanical and physical behavior of a complex system more accurately than the integer order model. Fractional singular systems within mixed integer and combined fractional derivatives are established in this paper. The fractional Lagrange equations, fractional primary constraints, fractional constrained Hamilton equations, and consistency conditions are analyzed. Then Noether and Lie symmetry methods are studied for finding the integrals of the fractional constrained Hamiltonian systems. Finally, an example is given to illustrate the methods and results.