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Keywords = Atangana–Baleanu fractional differences and sums

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13 pages, 291 KB  
Article
On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels
by Thabet Abdeljawad and Arran Fernandez
Mathematics 2019, 7(9), 772; https://doi.org/10.3390/math7090772 - 22 Aug 2019
Cited by 10 | Viewed by 2599
Abstract
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 [...] Read more.
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. Full article
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