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

  • Harbir Antil
    George Mason University
  • Mario Bencomo
    Rice University
  • Gunvant Birajdar
    Tata Institute of Social Sciences
  • 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
  • Yanlai Chen
    University of Massachusetts, Dartmouth
  • Zhen-Qing Chen
    University of Washington
  • 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
  • Mahmoud El-Borai
    Alexandria University Faculty of Science
  • Sergei Fedotov
    The University of Manchester
  • Nicolas Garcia Trillos
    Brown University
  • Roberto Garrappa
    University of Bari
  • Varsha Gejji
    Savitribai Phule Pune University
  • Thomas Goff
    Middle Tennessee State 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
  • Xianjuan Li
    FUZHOU University/BROWN UNIVERSITY
  • Changpin Li
    Shanghai University
  • Yulong Li
    University of Wyoming
  • Shangerganesh Lingeshwaran
    National Institute of Technology Goa
  • 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
  • Mohammad Mirzadeh
    MIT
  • Maryam Naghibolhosseini
    Michigan State University
  • Alberto Nogueira Junior
    IBM Research Brazil
  • Deepak Pachpatte
    Dr. Babasaheb Ambedkar Marathwada University
  • Guofei Pang
    Brown university
  • Jeungeun Park
    University of Iowa
  • Charles Parker
    Brown University
  • Camelia Pop
    University of Minnesota
  • Elizabeth Ramirez
    Columbia University
  • Sivaguru Ravindran
    University of Alabama in Huntsville
  • Enrico Scalas
    University of Sussex
  • Peter Scheffler
    University of Siegen
  • Jie Shen
    Purdue University
  • Joseph Shomberg
    Providence College
  • Fangying Song
    Brown University
  • Pablo Raúl Stinga
    Iowa State University
  • Yanhui Su
    Brown University
  • Tim Thompson
    The University of Waterloo
  • Tingting Wang
    Brown University
  • Nan Wang
    Brown University
  • Hong Wang
    University of South Carolina
  • 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 - 8:55Registration - 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

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