Lie symmetries and their inverse problems of nonholonomic Hamilton systems with fractional derivatives

• Theories of Lie symmetries are established for the fractional nonholonomic Hamilton systems.
• The inverse problems of Lie symmetries are first studied for the fractional dynamical systems.
• A series of theorems of Lie symmetries are obtained for these systems.

This letter focuses on studying Lie symmetries and their inverse problems of the fractional nonholonomic Hamilton systems. Based on the invariance of the fractional motion equations, constraint equations and virtual displacement restrictive conditions of the systems under the infinitesimal transformation with respect to the time and generalized coordinates, the Lie symmetries and conserved quantities of the fractional nonholonomic Hamilton system are discussed and the corresponding definitions, determining equations, limiting equations, additional restricting equations and Lie theorems are given. The letter also systematically studies inverse theorems of Lie symmetries of the fractional nonholonomic Hamilton systems. Finally, an example is discussed to illustrate theses results.