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.

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Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Harbir Antil
    George Mason University
  • Mario Bencomo
    Rice University
  • Animesh Biswas
    Iowa State University
  • Andrea Bonito
    Texas A&M University
  • Juan Pablo Borthagaray
    University of Maryland
  • Evan Camrud
    Iowa State University
  • Matthew Causley
    Kettering University
  • Cem Celik
    Dokuz Eylül University
  • YangQuan Chen
    UC Merced
  • Zhen-Qing Chen
    University of Washington
  • Yanlai Chen
    University of Massachusetts, Dartmouth
  • Brian Choi
    Boston University
  • Shue-Sum Chow
    Brigham Young University
  • Justin Crum
    University of Arizona
  • Marta D'Elia
    Sandia National Laboratories, NM
  • Weihua Deng
    Lanzhou University
  • Beichuan Deng
    Wayne State University
  • Sougata Dhar
    The University of Maine
  • Geoffrey Dillon
    University of South Carolina
  • Siwei Duo
    University of South Carolina
  • Sergei Fedotov
    The University of Manchester
  • Nicolas Garcia Trillos
    Brown University
  • Roberto Garrappa
    University of Bari
  • Varsha Gejji
    Savitribai Phule Pune University
  • Yiqi Gu
    Purdue University
  • Mamikon Gulian
    Brown University
  • Ling Guo
    Shanghai Normal University
  • Zhaopeng Hao
    Worcester Polytechnic Institute
  • Md Mehedi Hasan
    Brown University
  • Derek Hollenbeck
    University of California, Merced
  • Youngjoon Hong
    University of Illinois, Chicago
  • Xiaozhe Hu
    Tufts University
  • Fukeng Huang
    Purdue University
  • Olaniyi Iyiola
    Minnesota State University Moorhead
  • Jiahua Jiang
    University of Massachusetts Dartmouth
  • George Karniadakis
    Brown University
  • Nikolaos Kavallaris
    Brown University
  • James Kelly
    Michigan State University
  • Abdul Khaliq
    Middle Tennessee State University
  • Dustin Kremer
    University of Siegen
  • Svenja Lage
    Heinrich-Heine Universität Düsseldorf
  • Ying Li
    Missouri University of Science and Technology
  • Yulong Li
    University of Wyoming
  • Xianjuan Li
    FUZHOU University/BROWN UNIVERSITY
  • Changpin Li
    Shanghai University
  • Anna Lischke
    Brown University
  • Yuan Liu
    Mississippi State U
  • Yuri Luchko
    Beuth Hochschule für Technik
  • Marcin Magdziarz
    Wrocław University of Science and Technology
  • Francesco Mainardi
    University of Bologna
  • Zhiping Mao
    Brown University
  • Maryam Naghibolhosseini
    Michigan State University
  • Alberto Nogueira Junior
    IBM Research Brazil
  • Deepak Pachpatte
    Dr. Babasaheb Ambedkar Marathwada University
  • Jeungeun Park
    University of Iowa
  • Charles Parker
    Brown University
  • Camelia Pop
    University of Minnesota
  • Sivaguru Ravindran
    University of Alabama in Huntsville
  • Enrico Scalas
    University of Sussex
  • Peter Scheffler
    University of Siegen
  • Jie Shen
    Purdue University
  • Fangying Song
    Brown University
  • Pablo Raúl Stinga
    Iowa State University
  • Yanhui Su
    Brown University
  • Tim Thompson
    The University of Waterloo
  • Nan Wang
    Brown University
  • Hong Wang
    University of South Carolina
  • Tingting Wang
    Brown University
  • Mahamadi Warma
    University of Puerto Rico
  • Bruce West
    US Army Research Office
  • wuzhe xu
    University at Buffalo
  • Chuanju Xu
    Xiamen University
  • Mohsen Zayernouri
    Michigan State University
  • Yanzhi Zhang
    Missouri University of Sciences and Technology
  • Zhongqiang Zhang
    Worcester Polytechnic Institute
  • Kaixuan Zhang
    Brown University
  • Tinggang Zhao
    Lanzhou City University
  • Lifei Zhao
    Brown University
  • Yue Zhao
    Brown University
  • Tingtao Zhou
    Massachusetts Institute of Technology

Workshop Schedule

Monday, June 18, 2018
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
9:00 - 9:15am EDTWelcome - ICERM Director; followed by Mark Meerschaert11th Floor Lecture Hall 
9:15 - 10:00am EDTFractional Dynamics of Individuals in Complex Networks - Bruce West, US Army Research Office11th Floor Lecture Hall
10:15 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTFractional 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 - 12:15pm EDTEfficient and accurate numerical methods for solving fractional PDEs - Jie Shen, Purdue University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTAnomalous cumulative inertia and transport on network - Sergei Fedotov, The University of Manchester11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTOn the Bayesian formulation of fractional inverse problems and data-driven discretization of forward maps - Nicolas Garcia-Trillos, Brown University11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, June 19, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTFractional time equations and probabilistic representation - Zhen-Qing Chen, University of Washington11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTA new fractional process- A fractional non-homogeneous Poisson process - Enrico Scalas, Department of Mathematics, University of Sussex11th Floor Lecture Hall
11:30 - 12:15pm EDTThe obstacle problem for the fractional Laplacian with drift - Camelia Pop, University of Minnesota11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTNumerical Approximations of Fractional Operators using Dunford-Taylor Representations - Andrea Bonito, Texas A&M11th Floor Lecture Hall
3:30 - 5:00pm EDTPoster Session / Coffee Break11th Floor Collaborative Space 
Wednesday, June 20, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTMuntz Spectral Methods for Some Problems Having Singular Solutions - Chuanju Xu, Xiamen University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTNumerical methods for non-standard fractional operators in the simulation of dielectric materials - Roberto Garrappa, University of Bari, Italy11th Floor Lecture Hall
11:30 - 12:15pm EDTNonlocal Diffusion Operators for Normal and Anomalous Dynamics - Weihua Deng, Lanzhou University11th Floor Lecture Hall
12:40 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTNon-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 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTSpectral and Pseudo-Spectral Methods for Space-Time Distributed Fractional PDEs - Mohsen Zayernouri, Michigan State University11th Floor Lecture Hall
4:50 - 5:30pm EDTOpen Discussions 11th Floor Lecture Hall 
Thursday, June 21, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTMaximum principle for the fractional diffusion-wave equations and its applications - Yuri Luchko, Technical University of Applied Sciences Berlin11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTModeling of fractional dynamics using Levy walks - recent advances - Marcin Magdziarz, Wroclaw University of Science and Technology, Poland11th Floor Lecture Hall
11:30 - 12:15pm EDTOn nonlocal Monge--Ampère equations - Pablo Raúl Stinga, Iowa State University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
12:30 - 12:40pm EDTWorkshop Group Photo11th Floor Lecture Hall 
2:30 - 3:15pm EDTRegional observability of very slow diffusion processes - YangQuan Chen, University of California Merced11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTNumerical 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 - 9:45am EDTAnalysis 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 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTBoundary Conditions for Two-Sided Fractional Diffusion - James Kelly, Department of Statistics and Probability, Michigan State University11th Floor Lecture Hall
11:30 - 12:15pm EDTNonlocal, nonlinear, nonsmooth - Juan Pablo Borthagaray, University of Maryland11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTA fractional phase-field model using an infinitesimal generator of alpha stable Levy process - Siwei Duo, University of South Carolina11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTAdaptive Multilevel Finite Element Method for Fractional Differential Equations using Hierarchical Matric - Xiaozhe Hu, Tufts University11th Floor Lecture Hall

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

YangQuan Chen
UC Merced
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     Slides

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 University
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
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
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
University of Bologna
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