Research on fractional symmetry based on Riesz derivative

Abstract

The variational problem, Noether symmetry and conserved quantity, and Lie symmetry and conserved quantity of singular systems are investigated on the basis of Riesz derivatives. First, based on Riesz derivatives, the variational problem of Lagrangian systems is studied, the fractional Lagrange equation is established, and the primary constraint problem of the system is discussed when the Lagrangian is singular. Second, the constrained Hamilton equation is established and the compatibility condition is provided. Third, the Noether symmetry and conserved quantity and the Lie symmetry and conserved quantity of the constrained Hamiltonian system are studied. In the end, an example is provided for illustration.