336 citations · 1.1k across the 21 of their papers we have counts for
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On some analytic properties of tempered fractional calculus
Arran Fernandez, Ceren Ustaoglu
We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouvil…
A complex analysis approach to Atangana-Baleanu fractional calculus
Arran Fernandez
The standard definition for the Atangana-Baleanu fractional derivative involves an integral transform with a Mittag-Leffler function in the kernel. We show that this integral can b…
Analytical Development of Incomplete Riemann-Liouville Fractional Calculus
Arran Fernandez, Ceren Ustaoğlu, Mehmet Ali Özarslan
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegrati…
On fractional calculus with general analytic kernels
Arran Fernandez, Mehmet Ali Ozarslan, Dumitru Baleanu
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying i…
On a new class of fractional difference-sum operators based on discrete Atangana-Baleanu sums
Thabet Abdeljawad, Arran Fernandez
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…