Fractional Calculus on Time Scales

Details Fractional Calculus on Time Scales Fractional Calculus on Time Scales

2012-02-14

arxiv.org/abs/1202.2960v1

Mathematics

Classical Analysis and ODEs

PhD thesis, Doctoral Programme in Mathematics and Applications (PDMA), University of Aveiro and University of Minho, 2012. Sup

Scientific paper

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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