Noether and Lie Symmetry for Singular Systems Involving Mixed Derivatives

Abstract

Singular systems play an important role in many fields, and some new fractional operators, which are general, have been proposed recently. Therefore, singular systems on the basis of the mixed derivatives including the integer order derivative and the generalized fractional operators are studied. Firstly, Lagrange equations within mixed derivatives are established, and the primary constraints are presented for the singular systems. Then the constrained Hamilton equations are constructed by introducing the Lagrange multipliers. Thirdly, Noether symmetry, Lie symmetry and the corresponding conserved quantities for the constrained Hamiltonian systems are investigated. And finally, an example is given to illustrate the methods and results.