Special Issue on "Fractional PDEs: Theory, Numerics, and Applications"

Fractional Partial Differential Equations (FPDEs) are emerging as a powerful tool for modeling challenging multiscale phenomena including overlapping microscopic and macroscopic scales, anomalous transport, and long-range temporal or spatial interactions. The fractional order may be a function of space-time or even be a distribution, opening up tremendous opportunities for modeling and simulation of multiphysics phenomena, e.g. seamless transition from wave propagation to diffusion, or from local to non-local dynamics. It is even possible to construct data-driven fractional differential operators that fit data from a particular experiment or specific phenomenon, including the effect of uncertainties, in which the fractional orders are determined directly from the data. In other words, a new (and simple) data assimilation paradigm can be formulated to determine the fractional order (or possibly a distribution) by taking into account a diverse set of sources of information, including available experimental data albeit of variable fidelity.