  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.
