Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives
Abstract
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed classical/fractional Euler-Lagrange extremals. Both Lagrangian and Hamiltonian versions of the Noether theorem are obtained. Finally, we extend our Noether's theorem to more general problems of optimal control with classical and Riemann-Liouville derivatives.
Keywords
Cite
@article{arxiv.1209.1330,
title = {Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives},
author = {Gastao S. F. Frederico and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1209.1330},
year = {2013}
}
Comments
This is a preprint of a paper whose final and definite form will be published in: 51st IEEE Conference on Decision and Control, December 10-13, 2012, Maui, Hawaii, USA. Article Source/Identifier: PLZ-CDC12.1832.45c07804. Submitted 08-March-2012; accepted 17-July-2012. arXiv admin note: text overlap with arXiv:1001.4507