The fractional Laplacian in R d, which we write as (− Δ) α/2 with α∈(0, 2), has multiple
equivalent characterizations. Moreover, in bounded domains, boundary conditions must be …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

We present three schemes for the numerical approximation of fractional diffusion, which
build on different definitions of such a non-local process. The first method is a PDE approach …

In this paper, we generalize a one-dimensional fractional diffusion-wave equation to a one-
dimensional variable-order space-time fractional nonlinear diffusion-wave equation (V-OS …

Abstract Very recently Warma (2019 SIAM J. Control Optim. to appear) has shown that for
nonlocal PDEs associated with the fractional Laplacian, the classical notion of controllability …

Biologically inspired strategies have long been adapted to swarm robotic systems, including
biased random walks, reaction to chemotactic cues and long-range coordination. In this …

For some spatially nonlocal diffusion models with a finite range of nonlocal interactions
measured by a positive parameter δ, we review their formulation defined on a bounded …

For the discretization of the integral fractional Laplacian $(-\Delta)^ s $, $0< s< 1$, based on
piecewise linear functions, we present and analyze a reliable weighted residual a posteriori …

We prove trace and extension results for Sobolev-type function spaces that are well suited
for nonlocal Dirichlet and Neumann problems including those for the fractional $ p …

We propose a monotone discretization for the integral fractional Laplace equation on
bounded Lipschitz domains with the homogeneous Dirichlet boundary condition. The …