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

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.

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

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