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.
Academic Background
PhD
(Mathematics) Eastern Mediterranean University
February 27, 2020 - May 18, 2023
Honours and Awards
Publications
On tempered fractional calculus with respect to functions and the associated fractional differential equations
November 30, 2022
Ashwini D. Mali, Kishor D. Kucche, Arran Fernandez, Hafiz Muhammad Fahad,
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
Kishor D. Kucche, Ashwini D. Mali, Arran Fernandez, Hafiz Muhammad Fahad,
Chaos, Solitons and Fractals - Volume 163, Article Number 112547
On the importance of conjugation relations in fractional calculus
July 13, 2022
Arran Fernandez, Hafiz Muhammad Fahad,
Computational and Applied Mathematics - Volume 41, Issue 6, Article Number 246
Weighted Fractional Calculus: A General Class of Operators
April 07, 2022
Arran Fernandez, Hafiz Muhammad Fahad,
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
Hafiz Muhammad Fahad, Arran Fernandez,
Applied Mathematics and Computation - Volume:409,
On fractional calculus with analytic kernels with respect to functions
September 18, 2021
Christian Maxime Steve Oumarou, Hafiz Muhammad Fahad, Jean-Daniel Djida, Arran Fernandez,
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
Hafiz Muhammad Fahad, Mujeeb ur Rehman, Arran Fernandez,
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
Hafiz Muhammad Fahad, Arran Fernandez, Mujeeb-ur-Rehman, Maham Siddiqi,
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
Hafiz Muhammad Fahad, Arran Fernandez ,
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
Hafiz Muhammad Fahad, Mujeeb-ur-Rehman,
Bulletin of the Malaysian Mathematical Sciences Society - Pages 1-24
Conferences
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