  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.
