English

Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations

Optimization and Control 2010-10-28 v1

Abstract

We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that the solutions of the fractional problems coincide with the solutions of the corresponding non-fractional variational problems when the order of the discrete derivatives is an integer value.

Keywords

Cite

@article{arxiv.1007.0594,
  title  = {Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations},
  author = {Nuno R. O. Bastos and Rui A. C. Ferreira and Delfim F. M. Torres},
  journal= {arXiv preprint arXiv:1007.0594},
  year   = {2010}
}

Comments

Submitted 09-May-2009 to Discrete and Continuous Dynamical Systems (DCDS-B); revised 27-March-2010; accepted 04-July-2010