336 citations · 1.1k across the 21 of their papers we have counts for
23 papers
Unique axiomatisation of fractional integral operators on the real line
Ceren Özden, Arran Fernandez
The Cartwright--McMullen theorem (1978) establishes the uniqueness of the Riemann--Liouville family of fractional integral operators on a compact interval under a natural s…
Prabhakar-type linear differential equations with variable coefficients
Arran Fernandez, Joel E. Restrepo, Durvudkhan Suragan
Linear differential equations with variable coefficients and Prabhakar-type operators featuring Mittag-Leffler kernels are solved. In each case, the unique solution is constructed…
Weighted fractional calculus: a general class of operators
Arran Fernandez, Hafiz Muhammad Fahad
The operators of fractional calculus come in many different types, which can be categorised into general classes according to their nature and properties. We conduct a formal study…
Lipschitz and Fourier type conditions with moduli of continuity in rank 1 symmetric spaces
Arran Fernandez, Joel E. Restrepo, Durvudkhan Suragan
Sufficient and necessary results have been proven on Lipschitz type integral conditions and bounds of its Fourier transform for an function, in the setting of Riemannian symm…
On tempered fractional calculus with respect to functions and the associated fractional differential equations
Ashwini D. Mali, Kishor D. Kucche, Arran Fernandez +1
The prime aim of the present paper is to continue developing the theory of tempered fractional integrals and derivatives of a function with respect to another function. This theory…
A new representation for the solutions of fractional differential equations with variable coefficients
Arran Fernandez, Joel E. Restrepo, Durvudkhan Suragan
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite seri…
On fractional calculus with analytic kernels with respect to functions
Christian Maxime Steve Oumarou, Hafiz Muhammad Fahad, Jean-Daniel Djida +1
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be…
Fractional differential relations for the Lerch zeta function
Arran Fernandez, Jean-Daniel Djida
Starting from a recent result expressing the Lerch zeta function as a fractional derivative, we consider further fractional derivatives of the Lerch zeta function with respect to d…
A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators
Arran Fernandez, Cemaliye Kürt, Mehmet Ali Özarslan
We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function…
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…
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…
On some new properties of fractional derivatives with Mittag-Leffler kernel
Dumitru Baleanu, Arran Fernandez
We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearl…
Asymptotics to all orders of the Hurwitz zeta function
Arran Fernandez, Athanassios S. Fokas
We present several formulae for the large- asymptotics of the modified Hurwitz zeta function which are valid to all orders. In the case of $x…
Uniform asymptotics as a stationary point approaches an endpoint
Arran Fernandez, Athanassios S. Fokas, Euan A. Spence
We obtain the rigorous uniform asymptotics of a particular integral where a stationary point is close to an endpoint. There exists a general method introduced by Bleistein for obta…