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arXiv · 1005.0252

Discrete-Time Fractional Variational Problems

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 on the time scale $h\mathbb{Z}$, $h > 0$. 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 solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when $h$ tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation.

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Nuno R. O. Bastos, Rui A. C. Ferreira, Delfim F. M. Torres. 2010-05-03. Discrete-Time Fractional Variational Problems. https://doi.org/10.1016/j.sigpro.2010.05.001

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