Book of Abstracts: Fractional Calculus Seminar Series - Volume 2

Abstract

Fractional calculus is a multifaceted research topic, appealing to scientists ranging from pure mathematicians to physicists and biologists to engineers. The fundamen tal idea, of integro-differential operators of non-integer orders, is of interest both for the mathematical properties of such operators, generalising those of classical calcu lus, and for their applications in modelling problems involving non-local phenomena, which are often best captured using non-local operators. Due to the subject’s interest across a wide array of researchers from mathe maticians to practitioners, it becomes cumbersome for ideas to flow freely from one community to another. As a result, some results may be rediscovered multiple times in different areas, leading to redundant research, and the field risks growing in directions that may not be useful across the community. The Fractional Calcu lus Seminar Series aims to connect the fragmented community and build bridges between researchers looking at fractional calculus from different viewpoints, to en courage holistic growth of the field. Now, in the second year of the seminar series, the horizons are further ex panded. Many of last year’s seminars focused on fundamentals like general classes of fractional-calculus operators and the mainstream applications in turbulence and stochastic research. This year, our focus sessions have been on adjacent topics of mathematical and scientific research, such as special functions and operator the ory, whose connections to fractional calculus are strong and well known although they are not inherently fractional-calculus topics themselves, and also multifractals. There are several reasons to predict future connections between fractional calculus and multifractals: firstly, the obvious philosophical link, both of them being predi cated on interpolating a fundamental concept between the whole numbers; secondly, Benoit B. Mandelbrot, widely recognised as the father of fractals, also worked on fractional Brownian motion, and thus it is possible to predict a link via stochastic processes. We envision many exciting developments in fractional calculus and related fields of science in the near future. This motivates and inspires us in our attempts to collect and document some current developments in the field, and we hope that these resources would be helpful for the next generation of researchers. Our vision is for the research field of fractional calculus to grow in a sustainable and holistic fashion, rather than in many disjointed directions without interconnections.

Special Focus Topics: • 09Mayto06June2025(6talks): fractional calculus and special functions. • 13 June, 27 June, 22 August 2025 (3 talks): fractional calculus and function spaces. • 01, 08, 15 August, 12 September, 14, 21, 28 November, 5 December (8 talks): fractals and multifractals: theory and applications.