Fractional Partial Differential Equations for Conservation Laws and Beyond: Theory, Numerics, and Applications (Summary Technical Report, Sep 2015–Nov 2022)

Author(s):

Joseph Myers

Abstract:

The FY15 Multidisciplinary University Research Initiative topic “Fractional PDEs for Conservation Laws and Beyond: Theory, Numerics, and Applications” led by Professor George Karniadakis at Brown University was active from 16 September 2015 through 29 November 2022. The objective of the effort has been to develop a new rigorous theoretical and computational framework enabling end-to end fractional-order modeling of physical problems governed by conservation laws in large-scale simulations. Progress in the development of these fractional-order methods hold promise for more accurate modeling and prediction in systems involving unobserved processes or systems where the physics is not well-understood.