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Fractional differential equations: initialisation, singularity, and dimensions

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: 

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.

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