Fractional PDEs: Theory, Algorithms and Applications
(June 18 - 22, 2018)

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Description

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.

Organizing Committee

  • George Em Karniadakis
    (Brown University)
  • Francesco Mainardi
    (University of Bologna)
  • Mark Meerschaert
    (Michigan State University)
  • Jie Shen
    (Purdue University)
  • Hong Wang
    (University of South Carolina)