• 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)


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 of some new models of fractional calculus, and analytic number theory, specifically using asymptotic series methods to analyse the growth behaviour of the Riemann zeta function.

Selected Publications

  • Fernandez A, Baleanu D. A novel definition of fractional differintegrals with Mittag-Leffler kernel having a semigroup property. Filomat, under review.
  • Fernandez A, Baleanu D. The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag-Leffler kernel. Advances in Difference Equations, under review.
  • Fernandez A, Fokas AS, Spence EA. Uniform asymptotics as a stationary point approaches an endpoint. IMA Journal of Applied Mathematics, under review. Available from:
  • Baleanu D, Fernandez A. On some new properties of fractional derivatives with Mittag-Leffler kernel. Communications in Nonlinear Science and Numerical Simulation, under review.
  • Fernandez A, Fokas AS. Asymptotics to all orders of the Hurwitz zeta function. Preprint.
  • 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 2017;15: 1-12.

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.