On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels

Mathematics

Arran Fernandez¹  Thabet Abdeljawad² 

[1] Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, Cambridge CB3 0WA, UK;Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia;

关键词: discrete fractional calculus;    Atangana–Baleanu fractional differences and sums;    discrete Mittag–Leffler function;    discrete nabla Laplace transform;    binomial theorem;    iterated process;    discrete Dirac delta function;   

DOI  :  10.3390/math7090772

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown