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.

## Fractional differential equations: initialisation, singularity, and dimensions

Research Group:

Arran Fernandez

Institution:

Eastern Mediterranean University

Schedule:

Wednesday, January 25, 2023 - 16:00 to 17:00

Location:

A-133

Location:

Online only. Zoom link: https://sissa-it.zoom.us/j/7306190508

Abstract: