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

Thabet Abdeljawad, Arran Fernandez
2019 arXiv   pre-print
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
more » ... e-sum operators have this semigroup property as well.
arXiv:1901.08268v1 fatcat:xj7ivd5vq5brnkxbi6rqyu4wdy