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arXiv · 1007.0594

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

Nuno R. O. Bastos·Rui A. C. Ferreira·Delfim F. M. Torres
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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.

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Nuno R. O. Bastos, Rui A. C. Ferreira, Delfim F. M. Torres. 2010-07-04. Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations. https://doi.org/10.3934/dcds.2011.29.417

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