Herglotz type Noether theorems of nonholonomic systems with generalized fractional derivatives

• The Herglotz principle with generalized operators is discussed, and the Herglotz type equations for nonholonomic systems are established. • The Noether symmetries are studied and the conserved quantities are obtained. • The nonholonomic canonical systems are innvestigated, and the fractional Herglotz type canonical equations with the generalized operators and the Noether theorems are obtained. Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties. In this paper, the Herglotz principle with generalized operators is discussed, and the Herglotz type equations for nonholonomic systems are established. Then, the Noether symmetries are studied, and the conserved quantities are obtained. The results are extended to nonholonomic canonical systems, and the Herglotz type canonical equations and the Noether theorems are obtained. Two examples are provided to demonstrate the validity of the methods and results.