Noether symmetries and conserved quantities of fractional nonconservative singular systems

Abstract

The Noether theory of fractional nonconservative singular systems is studied based on fractional factor derivative method in form space. The Lagrange equations with fractional factor are established through the variational principle. The criterion equation and the conserved quantities are further studied according to the fractional order Hamilton action quantity maintain invariance under the infinitesimal transformation. Finally, an example is given to illustrate the application. The results show that comparing with the conservative systems, the nonconservative forces have impact on the Noether identity, but because of enhancing the invariance condition, it does not change the form of Noether type conserved quantities, at the same time, we use fractional factor method to study the nonconservative singular systems, some conclusions are highly natural consistent with the classical integer order singular systems, so the fractional factor can establish the connection between the fractional order systems and the integer order systems.