Fractional differential equations

Programme theme

Modelling based on differential equations of fractional order and related heavy-tailed probability distributions has recently witnessed a surge of interest due to their ability to model complex phenomena. Applications include modelling contamination of groundwater flow, the electrical dynamics of the heart and the design of new materials. Fractional differential equations capture effects going well beyond the range tractable by conventional concepts and tools, and it is increasingly recognised that this framework is on the way of becoming a new paradigm in scientific modelling. This programme sets out to investigate the multiple facets of space-time fractional dynamics and make significant progress in the description and deep understanding of this new phenomenology.

A common feature of the problems the programme aims to address is space-time non-locality. In a mathematical formulation, spatial non-locality means that the evaluation of the action of an operator on a function at a particular point in space generally depends also on its effect in far-away positions. A typical example is the fractional Laplacian, however, we will consider a whole range of possible non-local operators, which generally may have different qualitative behaviours. Temporal non-locality means that the future evolution depends on its past, which is described in terms of fractional (such as Caputo) time-derivatives.

A particular aspect in the attempt to mathematically capture these problems is that several complementary approaches are at hand. A natural framework is offered by integro-differential equations featuring integral kernels in space and/or time variables, and one path to follow is then an analysis in terms of singular integrals and related objects. Another possibility is a more operator-based analysis emphasising spectral properties of pseudo-differential operators. A third way is a probabilistic formulation in terms of Feynman-Kac-type representations, involving random processes with jump discontinuities. One of the main aims of the programme is to explore the interaction of these multiple approaches, and develop a common framework and new methodology.

The programme will focus on the following themes within three workshops: (1) Deterministic and Stochastic Fractional Differential Equations and Jump Processes, (2) Fractional Kinetics, Hydrodynamic Limits and Fractals, (3) Optimal Control in Fractional Dynamics. Within the final two workshops there will also be sessions addressing applications and computational aspects of fractional differential equations. These sessions will cover themes such as physics (transport phenomena, quantum optics), chemistry and biology (chemotaxis, population dynamics/foraging), environmental sciences (groundwater contamination, fractal solute transport), and technology (image reconstruction and signal analysis, financial engineering).

The programme intends to offer to scientists working broadly in the interdisciplinary area of fractional calculus, non-local equations, random processes with jumps, and their applications, a platform to interact and communicate their research results in a vibrant research environment. To strengthen intra- and inter-disciplinary cross-fertilisation, these topics will be organised in a way to combine key subjects of research with a double focus, including both theoretical aspects with more applied/computational interests. Participants to the programme and the workshops are expected from six continents, including a significant proportion of early career scientists. We also encourage PhD students/post-doctoral researchers to attend some of the proceeds or outreach activities.

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Click here to download the programme's final scientific report

FDE programme: interview with organisers Eulalia Nualart and Vassili Kolokoltsov

Preprints

Title	Year	Programme
A Varadhan estimate for big order differential generators Authors: Remi Leandre Download PDF	2021	FDE2	20 June 2022

Title

Year

Programme

A Varadhan estimate for big order differential generators

Authors: Remi Leandre

Download PDF

2021

FDE2

20 June 2022

Workshops

FD2W01

Seminars

Tuesday 25th January 2022
09:00 to 09:30	Eulalia Nualart Universitat Pompeu Fabra FDE2 Organiser talks - Non-existence of solutions to fractional stochastic heat equations	Room 2
09:30 to 10:00	Vassili Kolokoltsov University of Warwick Probabilistic representation for the solutions of generalized fractional equations and generalized operator-valued Mittag-Leffler functions	Room 2
10:00 to 10:30	Michael Roeckner Universität Bielefeld Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations	Room 2

Monday 31st January 2022
14:00 to 15:00	Arran Fernandez Eastern Mediterranean University On fractional Wirtinger derivatives for complex analysis	Room 2
18:00 to 19:00	George Anastassiou University of Memphis Abstract fractional monotone constrained bivariate approximation	Room 2

Monday 7th February 2022
14:00 to 15:00	Rico Zacher Universität Ulm Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel - Rico Zacher	Room 2
18:00 to 19:00	Eli Barkai Bar-Ilan University Fractional diffusion of cold atoms in optical lattices	Room 2

Monday 14th February 2022
09:00 to 10:00	Zdzislaw Brzezniak University of York Weak Martingale Solutions for the Stochastic Nonlinear Fractional Schrödinger Equations	Room 2
14:00 to 15:00	Igor Podlubny Technical University of Kosice On some interpretations of fractional-order operators	Room 2
17:00 to 18:00	Laura Sacerdote University of Torino On heavy tails propagation in an Integrate and Fire Network	Room 2

Monday 28th February 2022
09:00 to 10:00	Elina Shishkina Voronezh State University Random walks and fractional Euler-Poisson-Darboux equation	Room 2
14:00 to 15:00	Stanislav Molchanov University of North Carolina Random Schrödinger operator on fractals	Room 2
17:15 to 18:15	Francesco Mainardi University of Bologna Wright and Whittaker Functions in Time Fractional Diffusion Problems	Room 2
18:15 to 19:15	George Anastassiou University of Memphis Algebraic function based Banach space valued ordinary and fractional neural network approximations	Room 2

Wednesday 2nd March 2022
11:00 to 12:00	Avi Mayorcas University of Cambridge Blow-up criteria for an SPDE model of chemotaxis Speaker: Avi Mayorcas	Room 2

Monday 7th March 2022
10:00 to 11:00	Mladen Savov Sofia University St. Kliment Ohridski; Bulgarian Academy of Sciences Theory of Bernstein-Gamma functions and asymptotics of densities of exponential functionals of subordinators	Room 2
14:00 to 15:00	Kai Diethelm University of Applied Sciences Würzburg-Schweinfurt Diffusive Representations of Fractional Differential Operators and Their Use in Numerical Fractional Calculus	Room 2
18:00 to 19:00	George Anastassiou University of Memphis Generalized Fractional Ostrowski and Grüss type inequalities involving several Banach algebra valued functions	Room 2

Monday 14th March 2022
10:00 to 11:00	Xiaochuan Yang Brunel University Fractality and multifractality of Markov processes	Room 2
14:00 to 15:00	Bruno Toaldo Università degli Studi di Torino Semi-Markov approach to anomalous diffusion	Room 2
17:15 to 18:15	Giacomo Ascione Università degli Studi di Napoli Federico II Non-local Schrödinger operators with eigenvalues at the spectral edge	Room 2

Wednesday 16th March 2022
11:00 to 12:00	Jack Coughlin University of Washington Asymptotic-preserving dynamical low-rank discretization of kinetic plasma models (copy)	Room 2
13:00 to 14:00	Elizabeth Carlson University of Victoria Using Data to Accurately and Efficiently Model Turbulent Flows: Data Assimilation & Parameter Recovery	Room 2

Monday 28th March 2022
09:00 to 10:00	Blas M Vinagre Universidad de Extremadura There is Plenty of Fractional at the Botton: Fractional Calculus in Microrobotics	Room 2
10:00 to 11:00	Boris Baeumer University of Otago Intermittent non-linear systems with noise. A derivation from first principles.	Room 2
14:00 to 15:00	Yuliya Mishura Taras Shevchenko National University of Kyiv Limit theorems, financial applications and entropy of fractional Brownian motion: solved and unsolved problems	Room 2
17:15 to 18:15	Enrico Scalas University of Sussex A fractional generalisation of the Dirichlet distribution	Room 2

Monday 4th April 2022
10:00 to 11:00	Blas M Vinagre Universidad de Extremadura Feedback Control with Fractional Operators: Classical and Modern Control Approaches	Room 2
14:00 to 15:00	Maria Dolores Ruiz-Medina Universidad de Granada Functional time series approach for inference on multifractional partial pseudodifferential equations	Room 2
17:15 to 18:15	Mark Kelbert Higher School of Economics, Moscow; Swansea University On a mixed singular/switching control problem with multiple regimes	Room 2

Tuesday 5th April 2022
16:00 to 17:00	Stanislav Molchanov University of North Carolina Population dynamics and black spots on the Sun: Rothschild Lecture	Room 1

Thursday 7th April 2022
11:00 to 12:30	Stanislav Molchanov University of North Carolina Mini course: Spectral Theory on the Fractals: Lecture 1 - Fractal lattices. The Sierpinski lattice as a typical example. Random walks on these lattices.	Room 2

Monday 11th April 2022
09:00 to 10:00	Arran Fernandez Eastern Mediterranean University Semigroup properties for multi-dimensional fractional integral operators	Room 2
10:00 to 11:00	Vanja Wagner University of Zagreb Nonlocal regional operators and the corresponding stochastic processes	Room 2
11:00 to 12:30	Stanislav Molchanov University of North Carolina Mini course: Spectral Theory on the Fractals: Lecture 2 - Spectral theory on the above-mentioned lattices. Spectral dimension	Room 1
14:00 to 15:00	Remi Leandre Université de Franche-Comté Toward a Wong-Zakai approximation for big order generators	Room 2

Tuesday 12th April 2022
11:00 to 12:30	Stanislav Molchanov University of North Carolina Mini course: Spectral Theory on the Fractals: Lecture 3 - Schrödinger operator on the Sierpinski lattice with random potential (Anderson model). Cluster expansion on the resolvent. Localization theorem	Room 1

Wednesday 13th April 2022
11:00 to 12:00	Xiaochuan Yang Brunel University On some multifractal models (copy)	Room 2
13:00 to 14:00	Pavan Pranjivan Mehta Brown University Addressing anamolous diffusion of turbulent flows using fractional derivatives	Room 2

Thursday 14th April 2022
11:00 to 12:30	Stanislav Molchanov University of North Carolina Mini course: Spectral Theory on the Fractals: Lecture 4: Hierarchical models. Dyson lattice and the spectrum of the corresponding Laplacian.	Room 1

Monday 25th April 2022
09:30 to 10:30	Atsuhide Ishida Tokyo University of Science Mourre estimate for non-local Schrödinger operators	Room 2
11:00 to 12:30	Stanislav Molchanov University of North Carolina Mini course: Spectral Theory on the Fractals: Lecture 5 Continuous hierarchical models. Localization theorem for the class of the random potentials of the finite rank.	Room 2
14:00 to 15:00	Jinqiao Duan Illinois Institute of Technology Fractional Differential Equations Arising from Stochastic Dynamical Systems	Room 2
17:15 to 18:15	Diana Stan Universidad de Cantabria Carleman estimates for fractional relativistic operators	Room 2

Tuesday 26th April 2022
11:00 to 12:30	Stanislav Molchanov University of North Carolina Mini course: Spectral Theory on the Fractals: Lecture 6: Airy hierarchical model and its random perturbations.	Room 2

Wednesday 27th April 2022
16:00 to 17:00	Luisa Beghin University of Rome La Sapienza Non-local differential operators in probability - Kirk Lecture	Room 1

Wednesday 4th May 2022
11:00 to 12:00	William Golding University of Texas at Austin Uniqueness of shock waves under small perturbations for the Isentropic Euler Equations	Room 2
13:00 to 14:00	Antoine Remond-Tiedrez University of Cambridge (In)stability of an anisotropic micropolar fluid	Room 2

Wednesday 1st June 2022
11:00 to 12:00	Self-reinforcement, superdiffusion and subdiffusion	Room 2
13:00 to 14:00	Nonlocal quadratic forms with visibility constraint (joint work with Moritz Kassmann)	Room 2

Wednesday 8th June 2022
11:00 to 12:00	Jo Evans University of Warwick Steady states for the BGK equation in an interval	Room 2
13:00 to 14:00	Akhilesh Kumar Verma University of Warwick Akilesh Verma Lagrangian properties of the model plane-Couette flow	Room 2

Wednesday 15th June 2022
11:00 to 12:00	Daniel Boutros University of Cambridge On Energy Conservation for the hydrostatic Euler equations: an Onsager Conjecture	Room 2
13:00 to 14:00	Arran Fernandez Eastern Mediterranean University Adapting the Fokas transform method to solve certain fractional PDEs	Room 2

Wednesday 22nd June 2022
11:00 to 12:00	Santiago Benavides University of Warwick; Massachusetts Institute of Technology Phase Transitions in Geophysical Turbulence (copy)	Room 2
13:00 to 14:00	Oscar de Wit University of Cambridge Active Brownian Particles and Chemotaxis	Room 2

Organisers

Vassili Kolokoltsov University of Warwick
Jozsef Lörinczi Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
Eulalia Nualart Universitat Pompeu Fabra
Michael Roeckner Universität Bielefeld
Laura Sacerdote University of Torino

Speakers

George Anastassiou University of Memphis
Giacomo Ascione Università degli Studi di Napoli Federico II
Boris Baeumer University of Otago
Eli Barkai Bar-Ilan University
Luisa Beghin University of Rome La Sapienza
Santiago Benavides University of Warwick; Massachusetts Institute of Technology
Daniel Boutros University of Cambridge
Zdzislaw Brzezniak University of York
Elizabeth Carlson University of Victoria
Jack Coughlin University of Washington
Oscar de Wit University of Cambridge
Kai Diethelm University of Applied Sciences Würzburg-Schweinfurt
Jinqiao Duan Illinois Institute of Technology
Jo Evans University of Warwick
Arran Fernandez Eastern Mediterranean University
William Golding University of Texas at Austin
Atsuhide Ishida Tokyo University of Science
Mark Kelbert Higher School of Economics, Moscow; Swansea University
Vassili Kolokoltsov University of Warwick
Remi Leandre Université de Franche-Comté
Francesco Mainardi University of Bologna
Avi Mayorcas University of Cambridge
Yuliya Mishura Taras Shevchenko National University of Kyiv
Stanislav Molchanov University of North Carolina
Eulalia Nualart Universitat Pompeu Fabra
Igor Podlubny Technical University of Kosice
Pavan Pranjivan Mehta Brown University
Antoine Remond-Tiedrez University of Cambridge
Michael Roeckner Universität Bielefeld
Maria Dolores Ruiz-Medina Universidad de Granada
Laura Sacerdote University of Torino
Mladen Savov Sofia University St. Kliment Ohridski; Bulgarian Academy of Sciences
Enrico Scalas University of Sussex
Elina Shishkina Voronezh State University
Diana Stan Universidad de Cantabria
Bruno Toaldo Università degli Studi di Torino
Akhilesh Kumar Verma University of Warwick
Blas M Vinagre Universidad de Extremadura
Vanja Wagner University of Zagreb
Xiaochuan Yang Brunel University
Rico Zacher Universität Ulm

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Participants

George Anastassiou University of Memphis
Giacomo Ascione Università degli Studi di Napoli Federico II
Sigurd Assing University of Warwick
Abdon Atangana University of the Free State
Boris Baeumer University of Otago
Eli Barkai Bar-Ilan University
Luisa Beghin University of Rome La Sapienza
Elena Boguslavskaya Brunel University
Zdzislaw Brzezniak University of York
Jose A Carrillo University of Oxford
Dan Crisan Imperial College London
Kai Diethelm University of Applied Sciences Würzburg-Schweinfurt
Qiang Du Columbia University
Jinqiao Duan Illinois Institute of Technology
Hafiz Muhammad Fahad Eastern Mediterranean University
Sergei Fedotov University of Manchester
Arran Fernandez Eastern Mediterranean University
Dmitri Finkelshtein Swansea University
Neville Ford University of Chester
Tadahisa Funaki University of Tokyo
Sekhar Ghosh National Institute of Technology Rourkela
Mikhail Gomoyunov  N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences (IMM UB RAS)
Jorge Gonzalez-Cazares University of Warwick; The Alan Turing Institute
Patricia Gonçalves Instituto Superior Técnico, Lisboa
Daniel Han University of Manchester; University of Cambridge
Elena Hernández-Hernández Imperial College London
Astrid Hilbert Linnaeus University
Max Hongler EPFL - Ecole Polytechnique Fédérale de Lausanne
Atsuhide Ishida Tokyo University of Science
Saul Jacka University of Warwick
Sergey Kabanikhin Novosibirsk State University; Sobolev Institute of Mathematics
Mark Kelbert Higher School of Economics, Moscow; Swansea University
Rainer Klages Queen Mary University of London
Anatoly Kochubei National Academy of Sciences of Ukraine
Vassili Kolokoltsov University of Warwick
Valentin Konakov Higher School of Economics, Moscow; Moscow State University
Yuri Kondratiev Bielefeld University
Remi Leandre Université de Franche-Comté
Nikolai Leonenko Cardiff University
Wei Liu Jiangsu Normal University
Eugene Lytvynov Swansea University
Jozsef Lörinczi Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
Marcin Magdziarz Wroclaw University of Technology
Francesco Mainardi University of Bologna
Stéphane Menozzi Université Paris Saclay; Higher School of Economics, Moscow
Aleksandar Mijatovic University of Warwick
Yuliya Mishura Taras Shevchenko National University of Kyiv
Stanislav Molchanov University of North Carolina
Elzbieta Motyl Uniwersytet Lódzki
Roberta Musina Università degli Studi di Udine
Alexander Nazarov St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences; Saint Petersburg State University
Eulalia Nualart Universitat Pompeu Fabra
Maria Joao Oliveira University of Lisbon
Gianni Pagnini BCAM - Basque Center for Applied Mathematics
Leonid Pastur National Academy of Sciences of Ukraine; Institute for Low Temperatures, Kharkov
Andrey Piatnitski Universitetet i Tromsø; Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences
Gabriela Planas Universidade Estadual de Campinas
Igor Podlubny Technical University of Kosice
Pavan Pranjivan Mehta Brown University
Marco Rehmeier Bielefeld University
Michael Roeckner Universität Bielefeld
Luz Roncal BCAM - Basque Center for Applied Mathematics; Universidad del País Vasco
Maria Dolores Ruiz-Medina Universidad de Granada
Laura Sacerdote University of Torino
Abner Salgado University of Tennessee
Fatih Say Ordu University
Enrico Scalas University of Sussex
Andre Schenke Bielefeld University
Rene Schilling Technische Universität Dresden
Elina Shishkina Voronezh State University
Renat Sibatov Moscow Institute of Physics and Technology
Vittoria Sposini Universität Wien
Diana Stan Universidad de Cantabria
Oliver Street Imperial College London
Qing Tang None / Other
Bruno Toaldo Università degli Studi di Torino
Delfim F. M. Torres Universidade de Aveiro
Marianna Troeva North-Eastern Federal University
Jayme Vaz Universidade Estadual de Campinas
Blas M Vinagre Universidad de Extremadura
Vanja Wagner University of Zagreb
Xiaochuan Yang Brunel University
Rico Zacher Universität Ulm
Boguslaw Zegarlinski Université de Toulouse; CNRS (Centre national de la recherche scientifique)
Elena Zhizhina Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences
Enrique Zuazua Friedrich-Alexander-Universität Erlangen-Nürnberg

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Programme theme

FDE programme: interview with organisers Eulalia Nualart and Vassili Kolokoltsov

Preprints

A Varadhan estimate for big order differential generators

Workshops

Deterministic and stochastic fractional diﬀerential equations and jump processes

Fractional kinetics, hydrodynamic limits and fractals

Optimal control and fractional dynamics

Seminars

Organisers

Speakers

Participants

Supported By

Fractional differential equations

Programme theme

FDE programme: interview with organisers Eulalia Nualart and Vassili Kolokoltsov

Preprints

A Varadhan estimate for big order differential generators

Workshops

Deterministic and stochastic fractional diﬀerential equations and jump processes

Fractional kinetics, hydrodynamic limits and fractals

Optimal control and fractional dynamics

Seminars

Organisers

Speakers

Participants

Supported By

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