Organizing Committee
Abstract

Fractional partial differential equations (FPDEs) are emerging as a powerful tool for modeling challenging multiscale phenomena including overlapping microscopic and macroscopic scales. Compared to integer-order PDEs, the fractional order of the derivatives in FPDEs may be a function of space and time or even a distribution, opening up great opportunities for modeling and simulation of multi-physics phenomena, e.g. seamless transition from wave propagation to diffusion, or from local to non-local dynamics. In addition, data-driven fractional differential operators may be constructed to fit data from a particular experiment or specific phenomenon, including the effect of uncertainties. FPDEs lead to a paradigm shift, according to which data-driven fractional operators may be constructed to model a specific phenomenon instead of the current practice of tweaking free parameters that multiply pre-set integer-order differential operators. This workshop will cover all these areas, including (but not limited to) FPDE modeling, stochastic interpretation of FPDEs, efficient and accurate numerical solutions of FPDEs, mathematical analysis of FPDEs, and application of FPDE models.

Confirmed Speakers & Participants

Workshop Schedule

Monday, June 18, 2018
TimeEventLocationMaterials
8:30 - 8:55Registration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
9:00 - 9:15Welcome - ICERM Director; followed by Mark Meerschaert11th Floor Lecture Hall 
9:15 - 10:00Fractional Dynamics of Individuals in Complex Networks - Bruce West, US Army Research Office11th Floor Lecture Hall
10:15 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Fractional calculus via transcendental functions of the Mittag-Leffler and Wright type - Francesco Mainardi, Department of Physics and Astronomy, University of Bologna, Italy11th Floor Lecture Hall
11:30 - 12:15Efficient and accurate numerical methods for solving fractional PDEs - Jie Shen, Purdue University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Anomalous cumulative inertia and transport on network - Sergei Fedotov, The University of Manchester11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45On the Bayesian formulation of fractional inverse problems and data-driven discretization of forward maps - Nicolas Garcia-Trillos, Brown University11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, June 19, 2018
TimeEventLocationMaterials
9:00 - 9:45Fractional time equations and probabilistic representation - Zhen-Qing Chen, University of Washington11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15A new fractional process- A fractional non-homogeneous Poisson process - Enrico Scalas, Department of Mathematics, University of Sussex11th Floor Lecture Hall
11:30 - 12:15The obstacle problem for the fractional Laplacian with drift - Camelia Pop, University of Minnesota11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Numerical Approximations of Fractional Operators using Dunford-Taylor Representations - Andrea Bonito, Texas A&M11th Floor Lecture Hall
3:30 - 5:00Poster Session / Coffee Break11th Floor Collaborative Space 
Wednesday, June 20, 2018
TimeEventLocationMaterials
9:00 - 9:45Muntz Spectral Methods for Some Problems Having Singular Solutions - Chuanju Xu, Xiamen University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Numerical methods for non-standard fractional operators in the simulation of dielectric materials - Roberto Garrappa, University of Bari, Italy11th Floor Lecture Hall
11:30 - 12:15Nonlocal Diffusion Operators for Normal and Anomalous Dynamics - Weihua Deng, Lanzhou University11th Floor Lecture Hall
12:40 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Non-symmetric fractional operators as special cases of nonlocal convection-diffusion operators- analysis and applications. - Marta D'Elia, Sandia National Laboratories11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Spectral and Pseudo-Spectral Methods for Space-Time Distributed Fractional PDEs - Mohsen Zayernouri, Michigan State University11th Floor Lecture Hall
4:50 - 5:30Open Discussions 11th Floor Lecture Hall 
Thursday, June 21, 2018
TimeEventLocationMaterials
9:00 - 9:45Maximum principle for the fractional diffusion-wave equations and its applications - Yuri Luchko, Technical University of Applied Sciences Berlin11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Modeling of fractional dynamics using Levy walks - recent advances - Marcin Magdziarz, Wroclaw University of Science and Technology, Poland11th Floor Lecture Hall
11:30 - 12:15On nonlocal Monge--Ampère equations - Pablo Raúl Stinga, Iowa State University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
12:30 - 12:40Workshop Group Photo11th Floor Lecture Hall 
2:30 - 3:15Regional observability of very slow diffusion processes - YangQuan Chen, University of California Merced11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Numerical methods for the multi-dimensional fractional Laplacian and their applications - Yanzhi Zhang, Missouri University of Science and Technology11th Floor Lecture Hall
Friday, June 22, 2018
TimeEventLocationMaterials
9:00 - 9:45Analysis of the controllability of space-time fractional diffusion and super diffusion equations. - Mahamadi Warma, University of Puerto Rico, Rio Piedras Campus11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Boundary Conditions for Two-Sided Fractional Diffusion - James Kelly, Department of Statistics and Probability, Michigan State University11th Floor Lecture Hall
11:30 - 12:15Nonlocal, nonlinear, nonsmooth - Juan Pablo Borthagaray, University of Maryland11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15A fractional phase-field model using an infinitesimal generator of alpha stable Levy process - Siwei Duo, University of South Carolina11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Adaptive Multilevel Finite Element Method for Fractional Differential Equations using Hierarchical Matric - Xiaozhe Hu, Tufts University11th Floor Lecture Hall

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Lecture Videos

Adaptive Multilevel Finite Element Method for Fractional Differential Equations using Hierarchical Matric

Xiaozhe Hu
Tufts University
June 22, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

A fractional phase-field model using an infinitesimal generator of alpha stable Levy process

Siwei Duo
University of South Carolina
June 22, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

Nonlocal, nonlinear, nonsmooth

Juan Pablo Borthagaray
University of Maryland
June 22, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Boundary Conditions for Two-Sided Fractional Diffusion

James Kelly
Michigan State University
June 22, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Analysis of the controllability of space-time fractional diffusion and super diffusion equations

Mahamadi Warma
University of Puerto Rico
June 22, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Numerical methods for the multi-dimensional fractional Laplacian and their applications

Yanzhi Zhang
Missouri University of Sciences and Technology
June 21, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

Regional observability of very slow diffusion processes

YangQuan Chen
UC Merced
June 21, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

On nonlocal Monge--Ampère equations

Pablo Raúl Stinga
Iowa State University
June 21, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Modeling of fractional dynamics using Levy walks - recent advances

Marcin Magdziarz
Wrocław University of Science and Technology
June 21, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

Maximum principle for the fractional diffusion-wave equations and its applications

Yuri Luchko
Beuth Hochschule für Technik
June 21, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Spectral and Pseudo-Spectral Methods for Space-Time Distributed Fractional PDEs

Mohsen Zayernouri
Michigan State University
June 20, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

Non-symmetric fractional operators as special cases of nonlocal convection-diffusion operators- analysis and applications.

Marta D'Elia
Sandia National Laboratories, NM
June 20, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Nonlocal Diffusion Operators for Normal and Anomalous Dynamics

Weihua Deng
Lanzhou University
June 20, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

Numerical methods for non-standard fractional operators in the simulation of dielectric materials

Roberto Garrappa
University of Bari
June 20, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Muntz Spectral Methods for Some Problems Having Singular Solutions

Chuanju Xu
Xiamen University
June 20, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Numerical Approximations of Fractional Operators using Dunford-Taylor Representations

Andrea Bonito
Texas A&M
June 19, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

The obstacle problem for the fractional Laplacian with drift

Camelia Pop
University of Minnesota
June 19, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

A new fractional process- A fractional non-homogeneous Poisson process

Enrico Scalas
Department of Mathematics, University of Sussex
June 19, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Fractional time equations and probabilistic representation

Zhen-Qing Chen
University of Washington
June 19, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

On the Bayesian formulation of fractional inverse problems and data-driven discretization of forward maps

Nicolas Garcia Trillos
Brown University
June 18, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Anomalous cumulative inertia and transport on network

Sergei Fedotov
The University of Manchester
June 18, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

Efficient and accurate numerical methods for solving time fractional PDEs

Jie Shen
Purdue University and Xiamen University
June 18, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides

Fractional calculus via transcendental functions of the Mittag-Leffler and Wright type

Francesco Mainardi
Department of Physics and Astronomy, University of Bologna, Italy
June 18, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract

Fractional Dynamics of Individuals in Complex Networks

Bruce West
US Army Research Office
June 18, 2018
Fractional PDEs: Theory, Algorithms and Applications
Play     Abstract     Slides