Approximate Noether's symmetry and conservation laws for approximate Lagrangian systems on time scales

In this paper, the approximate Noether symmetries and conservation laws for approximate Lagrangian systems on time scales are discussed and presented. The Hamilton principle of approximate Lagrangian systems on time scales is given, and the approximate Lagrange equations for approximate Lagrangian systems on time scales are established. The Noether identities on time scales are given, the relationship between the approximate Noether symmetries and approximate conservation laws on time scales are established, the approximate inverse Noether theorems on time scales are obtained. Special cases such as the classical approximate Lagrangian systems and the discrete approximate Lagrangian systems are discussed. Finally, one example is given to illustrate the application of the results.