Fractional difference operators with discrete generalized Mittag–Leffler kernels

In this article we define fractional difference operators with discrete generalized Mittag–Leffler kernels of the form (Eθ,μ¯γ(λ,t−ρ(s)) for both Riemann type (ABR) and Caputo type (ABC) cases, where AB stands for Atangana–Baleanu. Then, we employ the discrete Laplace transforms to formulate their corresponding AB−fractional sums, and prove useful and applicable versions of their semi-group properties. The action of fractional sums on the ABC...