Speaker: Arran Fernandez, Department of Mathematics, Eastern Mediterranean University, Famagusta, Northern Cyprus

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom :  A zoom meeitng link will appear here, one hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  fractional PDEs, unified transform method, complex analysis

Abstract: The unified transform method, or Fokas method, was developed by Athanassios Fokas during the late 1990s, as a method for solving PDEs explicitly using multi-dimensional transforms and complex contour deformations. It has been used to solve various linear and non-linear PDEs, and lends itself well to numerical evaluation in cases where exact calculation is unfeasible. Some years ago, we extended this method to certain families of fractional PDEs, involving a single time derivative and a linear combination of Riemann--Liouville fractional space derivatives. The method is significantly harder to apply in the fractional setting, due to the loss of many nice properties of polynomials which are now replaced by combinations of fractional power functions. This talk will provide an overview of Fokas's method in the classical setting, and then show our work in the fractional setting, with some pointers towards related problems that remain unsolved.

Biography: Arran Fernandez is a pure mathematician and associate professor at the Eastern Mediterranean University, specialising in fractional calculus. He completed his bachelor's, master's, and PhD at the University of Cambridge, where he began as the youngest student at the university (aged 15) and came top of his year to be the youngest-ever senior wrangler. Since completing his PhD in 2018, he has worked at the Eastern Mediterranean University, firstly as an assistant professor and then as an associate professor. He also spent a year working at Sultan Qaboos University, also as an associate professor. His research interests lie in connecting fractional calculus with other branches of mathematics, such as abstract algebra, analytic number theory, and Clifford analysis. His achievements in these directions include extending Mikusinski’s operational calculus to fractional PDEs, expressing the Riemann zeta function as a fractional differintegral of an elementary function, and defining fractional d-bar derivatives in complex and hypercomplex settings.

Bibliography