## Career

Full-time academic study to date:

**2014-present:**PhD student, DAMTP, University of Cambridge**2013-2014:**MMath/Part III student, DAMTP, University of Cambridge – graduated with distinction**2010-2013:**BA student, Cambridge Mathematical Tripos – youngest ever Senior Wrangler (highest-scoring student in finals)

Shorter research visits include:

**Sep-Oct 2017:**Çankaya University, Ankara, Turkey**Dec 2013:**University of Otago, Dunedin, New Zealand

## Research

Arran is a member of the Department of Applied Mathematics and Theoretical Physics. His current research interests are in the theory of **fractional calculus** (differentiation and integration to non-integer orders), including its application to partial differential equations and also the analysis and development of some new models of fractional calculus, and **analytic number theory** (the use of techniques from analysis to prove results significant for number theory), specifically using asymptotic analysis to analyse the growth behaviour of the Riemann zeta function and its generalisations.

## Selected Publications

- Fernandez A.
**The Lerch zeta function as a fractional derivative.***Banach Center Publications*, accepted 2018. Preprint available from: arXiv. - Fernandez A, Fokas AS.
**Asymptotics to all orders of the Hurwitz zeta function.***Journal of Mathematical Analysis and Applications*465(1) (2018), pp. 423-458. Accepted 2018; preprint available from: arXiv. - Fernandez A.
**An elliptic regularity theorem for fractional partial differential operators.***Computational and Applied Mathematics (*2018). Preprint available from: arXiv. - Fernandez A, Baleanu D.
**The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag-Leffler kernel.***Advances in Difference Equations*, 2018:86 (2018). - Fernandez A, Fokas AS, Spence EA.
**Uniform asymptotics as a stationary point approaches an endpoint.***IMA Journal of Applied Mathematics*83(1) (2018), pp. 204-242. Accepted 2017; preprint available from: arXiv. - Baleanu D, Fernandez A.
**On some new properties of fractional derivatives with Mittag-Leffler kernel.***Communications in Nonlinear Science and Numerical Simulation*59 (2018), pp. 444-462. Accepted 2017; preprint available from: arXiv. - Baleanu D, Fernandez A.
**A generalisation of the Malgrange-Ehrenpreis theorem to find fundamental solutions to fractional PDEs.***Electronic Journal of Qualitative Theory of Differential Equations*15 (2017), pp. 1-12. - Fernandez A, Baleanu D, Srivastava HM.
**Series representations for models of fractional calculus involving generalised Mittag-Leffler functions.***Communications in Nonlinear Science and Numerical Simulation*, under review. - Fernandez A, Baleanu D.
**On a new definition of fractional differintegrals with Mittag-Leffler kernel.***Filomat*, under review.

## Other activities

Arran is also the founder and current President of the Clare Hall Mathematical Association, a graduate student society based at Clare Hall college in Cambridge.