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

Abstract In Acosta etal.(2017), a complete n-dimensional finite element analysis of the
homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here …

The usual classical polynomials-based spectral Galerkin and Petrov–Galerkin methods
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …

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 …

We present a simple discretization scheme for the hypersingular integral representa-tion of
the fractional Laplace operator and solver for the corresponding fractional Laplacian …

We prove Besov regularity estimates for the solution of the Dirichlet problem involving the
integral fractional Laplacian of order s in bounded Lipschitz domains Ω:‖ u‖ B˙ 2,∞ s+ r …

We investigate a spectral Galerkin method for the fractional advection-diffusion-reaction
equations in one dimension. We first prove sharp regularity estimates of solutions in …

This paper describes the state of the art and gives a survey of the wide literature published
in the last years on the fractional Laplacian. We will first recall some definitions of this …

In this article we investigate the regularity of the solution to the fractional diffusion, advection,
reaction equation on a bounded domain in R 1. The analysis is performed in the weighted …

We prove exponential convergence in the energy norm of-finite element discretizations for
the integral fractional Laplacian of order subject to homogeneous Dirichlet boundary …