A Proper Extension of Noether’s Symmetry Theorem for Nonsmooth Extremals of the Calculus of Variations

A Proper Extension of Noether’s Symmetry Theorem for Nonsmooth Extremals of the Calculus of Variations

Noether’s Symmetry Theorem for Variational and Optimal Control Problems with Time Delay

We extend the DuBois–Reymond necessary optimality condition and Noether’s symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether’s theorem are proved, covering problems of the calculus of variations and optimal control with delays.

Non-conservative Noether’s theorem for fractional action-like variational problems with intrinsic and observer times

We extend Noether’s symmetry theorem to fractional action-like variational problems with higher-order derivatives.

Constants of motion for fractional action-like variational problems

We extend Noether’s symmetry theorem to the fractional RiemannLiouville integral functionals of the calculus of variations recently introduced by El-Nabulsi. AMS Subject Classification: 49K05, 49S05, 70H33.

Noether ’ s Theorem on Time Scales ?

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective EulerLagrange extremals.