Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains

Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations

Abstract. We consider a fractional Laplacian defined in bounded domains by the eigendecomposition of the integer-order Laplacian, and demonstrate how to compute very accurately (using the spectral element method) the eigenspectrum and corresponding eigenfunctions in twodimensional prototype complex-geometry domains. We then employ these eigenfunctions as trial and test bases to first solve the ...

Fractional Cauchy problems on bounded domains

Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain D ⊂ Rd with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional ti...

Space–time fractional diffusion on bounded domains

Distributed-order fractional diffusions on bounded domains

Fractional Generalized Random Fields on Bounded Domains

Using the theory of generalized random fields on fractional Sobolev spaces on bounded domains, and the concept of dual generalized random field, this paper introduces a class of random fields with fractional-order pure point spectra. The covariance factorization of an a-generalized random field having a dual is established, leading to a white-noise linearfilter representation, which reduces to ...