336 citations · 1.1k across the 21 of their papers we have counts for
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Solving PDEs of fractional order using the unified transform method
Arran Fernandez, Dumitru Baleanu, Athanassios S. Fokas
We consider the unified transform method, also known as the Fokas method, for solving partial differential equations. We adapt and modify the methodology, incorporating new ideas w…
On a new definition of fractional differintegrals with Mittag-Leffler kernel
Arran Fernandez, Dumitru Baleanu
We introduce and study the properties of a new family of fractional differential and integral operators which are based directly on an iteration process and therefore satisfy a sem…
Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions
Arran Fernandez, Dumitru Baleanu, H. M. Srivastava
We consider an integral transform introduced by Prabhakar, involving generalised multi-parameter Mittag-Leffler functions, which can be used to introduce and investigate several di…
Diffusion on middle- Cantor sets
Alireza Khalili Golmankhaneh, Arran Fernandez, Ali Khalili Golmankhaneh +1
In this paper, we study -calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions…
The Lerch zeta function as a fractional derivative
Arran Fernandez
We derive and prove a new formulation of the Lerch zeta function as a fractional derivative of an elementary function. We demonstrate how this formulation interacts very naturally…
An elliptic regularity theorem for fractional partial differential operators
Arran Fernandez
We present and prove a version of the elliptic regularity theorem for partial differential equations involving fractional Riemann-Liouville derivatives. In this case, regularity is…