Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by El-Nabulsi. First, the El-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and El-Nabulsi-Hamilton's canonical equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of El-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of El-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Finally, Noether's theorems for the non-conservative Hamilton system under the El-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.