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We formulate a new class of fractional difference and sum operators, studytheir fundamental properties, and find their discrete Laplace transforms. Themethod depends on iterating the fractional sum operators corresponding tofractional differences with discrete Mittag-Leffler kernels. The iterationprocess depends on the binomial theorem. We note in particular the fact thatthe iterated fractional sums have a certain semigroup property and hence thenew introduced iterated fractional difference-sum operators have this semigroupproperty as well.

On a new class of fractional difference-sum operators based on discrete Atangana-Baleanu sums