Fractional differential equations: initialisation, singularity, and dimensions - Arran Fernandez

Date : 25 January 2023
Title : Fractional differential equations:initialisation, singularity, and dimensions
Speaker : Prof Arran Fernandez, Eastern Mediterranean University, Cyprus

Organizers : Pavan Pranjivan Mehta (SISSA), Prof. Andrea Cangiani (SISSA)
Hosted at : SISSA, International School of Advanced Studies, Trieste, Italy

Cite as : Fernandez, A. (2023). Fractional differential equations: initialisation, singularity, and dimensions. at SISSA, Italy

Abstract: Generalising orders of differentiation and integration is very popular nowadays, but some fundamental issues need to be addressed when extending operators and differential equations to fractional orders. If an nth-order differential equation requires n initial conditions, then how many initial conditions does a fractional-order differential equation need, and of what type? If a fractional derivative is defined using an integral from the initial point to the independent variable, how is it possible to choose any initial condition at all? Real-world models should be dimensionally consistent, but what happens to the dimensions when fractional derivatives are involved? All of these questions and more will be addressed in this overview: starting from the basics of fractional calculus, proceeding to some fresh new ideas, and leaving open some questions concerning stochastic properties and applications.

Bio: Arran Fernandez is an associate professor in mathematics at the Eastern Mediterranean University in Northern Cyprus. Previously he was at the University of Cambridge, where he started in 2010 as the youngest student for over 200 years, graduating in 2013 as the youngest ever to top the mathematical tripos, and in 2018 with a PhD in fractional calculus and analytic number theory. His current research interests are primarily in fractional calculus, including its relationships with complex analysis, abstract algebra, special functions, analytic number theory, Clifford analysis, and other branches of pure mathematics.