237 citations · 538 across the 32 of their papers we have counts for
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On discrete generalized nabla fractional sums and differences
Pshtiwan Othman Mohammed, Thabet Abdeljawad, Faraidun Kadir Hamasalh
This article investigates a class of discrete nabla fractional operators by using the discrete nabla convolution theorem. Inspired by this, we define the discrete generalized nabla…
Mild and classical solutions for fractional evolution differential equation
J. Vanterler da C. Sousa, Thabet Abdeljawad, D. S. Oliveira
Investigating the existence, uniqueness, stability, continuous dependence of data among other properties of solutions of fractional differential equations, has been the object of s…
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…
Existence of mild solutions to Hilfer fractional evolution equations in Banach space
J. Vanterler da C. Sousa
In this paper, we investigate the existence of mild solutions to Hilfer fractional equation of semi-linear evolution with non-instantaneous impulses, using the concepts of equicont…
Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations
Thabet Abdeljawad, Raziye Mert, Delfim F. M. Torres
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational…
Sturm Liouville Equations in the frame of fractional operators with Mittag-Leffler kernels and their discrete versions
Raziye Mert, Thabet Abdeljawad, Allan Peterson
Very recently, some authors have studied new types of fractional derivatives whose kernels are nonsingular. In this article, we study Sturm-Liouville Equations () in the fram…