On a New Definition of Fractional Differintegrals with Mittag-Leffler Kernel - Fernandez, Arran; Baleanu, Dumitru (Univ Nis, Fac Sci Math, 2019)
We introduce a new family of fractional differential and integral operators which emerge from a fractional iteration process applied to some existing fractional operators with Mittag-Leffler kernels. We analyse the new operators and prove various facts about them, including a semigroup property. We also solve some ODEs in this new model by using Laplace transforms, and discuss applications of our results.
Keywords: fractional calculus; semigroup property; Mittag-Leffler function