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 …

Gaussian processes and random fields have a long history, covering multiple approaches to
representing spatial and spatio-temporal dependence structures, such as covariance …

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

The survey is devoted to numerical solution of the equation A α u= f, 0< α< 1, where A is a
symmetric positive definite operator corresponding to a second order elliptic boundary value …

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 …

The purpose of this work is to study solution techniques for problems involving fractional
powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary …

Variable-order space-time fractional diffusion equations, in which the variation of the
fractional orders determined by the fractal dimension of the media via the Hurst index …

The analysis of nonlocal discrete equations driven by fractional powers of the discrete
Laplacian on a mesh of size h> 0 (− Δ h) su= f, for u, f: Z h→ R, 0< s< 1, is performed. The …

We propose a new nonconforming finite element algorithm to approximate the solution to the
elliptic problem involving the fractional Laplacian. We first derive an integral representation …

The fractional Laplacian in R^ d has multiple equivalent characterizations. Moreover, in
bounded domains, boundary conditions must be incorporated in these characterizations in …