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arXiv · 1202.2960

Fractional Calculus on Time Scales

Nuno R. O. Bastos
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Abstract

We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. We also give new definitions of fractional derivatives and integrals on time scales via the inverse generalized Laplace transform.

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Nuno R. O. Bastos. 2012-02-14. Fractional Calculus on Time Scales. https://arxiv.org/abs/1202.2960

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