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

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

2010-07-04

arxiv.org/abs/1007.0594v1

Discrete Contin. Dyn. Syst. 29 (2011), no. 2, 417--437

Mathematics

Optimization and Control

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

Scientific paper

10.3934/dcds.2011.29.417

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.

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