  We formulate a new class of fractional difference and sum operators, study
their fundamental properties, and find their discrete Laplace transforms. The
method depends on iterating the fractional sum operators corresponding to
fractional differences with discrete Mittag-Leffler kernels. The iteration
process depends on the binomial theorem. We note in particular the fact that
the iterated fractional sums have a certain semigroup property and hence the
new introduced iterated fractional difference-sum operators have this semigroup
property as well.
