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

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

Nonlocal, nonlinear, nonsmooth

Juan Pablo Borthagaray
University of Maryland
June 22, 2018

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