Noether theorems for two fractional singular systems are discussed. One system involves mixed integer and Caputo derivatives, the other only derivatives. Firstly, primary constraints constrained Hamilton equations given. Then, of established, including identities, quasi-identities conserved quantities. Finally, results obtained illustrated by examples.

Singular systems behave more powerfully in terms of dynamical system modeling than ordinary state space systems. Since the algebraic equations in singular models can describe the systems constraints, nonlinear singular systems can present a general method for modeling and controlling constrained dynamical systems. This paper discusses an adaptive control for nonlinear singular systems which sat...