Summary
The primary focus of my research encompasses topics from special functions, partial differential equations, and operational and fractional calculus. More exactly, I am working on understanding the mathematical structure of fractional calculus, connections between the different types of operators and their generalisations, and specifically on fractional calculus with respect to functions and the corresponding differential equations, including generalised function spaces and regularity results. I am now driving these theoretical developments into the realm of interdisciplinary modelling, where I collaborate with movement ecologists to apply fractional calculus in developing novel models for animal movement and interaction.
Academic Background
PhD
(Mathematics) Eastern Mediterranean University
February 27, 2020 - May 18, 2023
Honours and Awards
Publications
An Extensive Study of Weighted Hilfer Fractional Calculus With Respect to Functions
January 15, 2026
Mathematical Methods in the Applied Sciences - Volume:49, Issue:1, Page:392-404
Transmuted fractional calculus with analytic kernels
December 01, 2025
Fractional Calculus and Applied Analysis - Volume:28, Issue:6, Page:3117-3151
On the generalised Erdélyi–Kober fractional operators
October 15, 2025
Computational and Applied Mathematics - Volume 45, Article Number 66
On Weighted Fractional Calculus With Respect to Functions
December 16, 2024
Mathematical Methods in the Applied Sciences - Volume:48, Issue:05, Pages:5642-5659
On tempered fractional calculus with respect to functions and the associated fractional differential equations
November 30, 2022
Mathematical Methods in the Applied Sciences - Volume 45, Issue 17, Pages 11134-11157
On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations
October 01, 2022
Chaos, Solitons and Fractals - Volume 163, Article Number 112547
On the importance of conjugation relations in fractional calculus
July 13, 2022
Computational and Applied Mathematics - Volume 41, Issue 6, Article Number 246
Weighted Fractional Calculus: A General Class of Operators
April 07, 2022
Fractal and Fractional - Volume 6, Issue 4, Article Number 208
Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations
November 15, 2021
Applied Mathematics and Computation - Volume:409,
On fractional calculus with analytic kernels with respect to functions
September 18, 2021
Computational and Applied Mathematics - Volume 40, Issue 7, Article Number 244
On Laplace transforms with respect to functions and their applications to fractional differential equations
September 12, 2021
Mathematical Methods in the Applied Sciences - Volume:46, Issue:07, Pages:8304-8323, 15 May 2023
Tempered and Hadamard-Type Fractional Calculus with Respect to Functions
June 02, 2021
Mediterranean Journal of Mathematics - Volume 18, Article Number: 143
Operational calculus for the Riemann–Liouville fractional derivative with respect to a function and its applications
April 01, 2021
Fractional Calculus and Applied Analysis - Volume 24, Issue 2, Pages 518-540
Generalized Substantial Fractional Operators and Well-Posedness of Cauchy Problem
September 21, 2020
Bulletin of the Malaysian Mathematical Sciences Society - Pages 1-24
Conferences
General Transmutation Relations and Their Applications
July 09, 2024 - July 12, 2024
Arran Fernandez, Hafiz Muhammad Fahad,
12th IFAC Conference on Fractional Differentiation and its Applications
A Historical Survey of Fractional Calculus with Respect to Functions (ψ-fractional Calculus)
July 31, 2023 - August 04, 2023
A. Fernandez, Hafiz Muhammad Fahad,
Operator Theory: Advances and Applications
Teaching Assistant
Eastern Mediterranean University, Northern Cyprus, Turkey
October 01, 2022 - June 01, 2023
Associate Lecturer
The Islamia University of Bahawalpur, Pakistan
October 01, 2020 - January 01, 2022