Noether symmetry method for Hamiltonian mechanics involving generalized operators (Q2051946)

The Agrawal generalized operators, fractional differential operators including Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo operators, are here employed to determine generalized Hamiltonian mechanics and generalized Noether theorems. Left and right generalized operators are briefly introduced, along with the corresponding Hamilton equations. The Noether theorem is then formulated, in the Hamiltonian setting, for the left and right generalized operators, with and without gauge function. The existence of adiabatic invariants of the generalized Hamilton equations is characterized by the existence of a suitable gauge function. As examples, invariants and adiabatic invariants are determined for the 2D isotropic harmonic oscillator and the Lotka biochemical oscillator.