In this work we study the finite difference method for the fractional diffusion equation with
high-dimensional hyper-singular integral fractional Laplacian. We first propose a simple and …

A generalised fractional derivative (the ψ-Caputo derivative) is studied. Generalisations of
standard discretisations are constructed for this derivative: L1, L1-2, L2-1 σ for derivatives of …

In this paper, we develop a conditional Monte Carlo method for solving PDEs involving an
integral fractional Laplacian on any bounded domain in arbitrary dimensions. We first …

In this work, we revisit the spectral Petrov-Galerkin method for fractional elliptic equations
with the general fractional operators. To prove the optimal convergence of the method, we …

We consider collocation methods for fractional elliptic equations with the integral fractional
Laplacian on general bounded domains using radial basis functions (RBFs). Leveraging the …

We present a highly accurate and efficient spectral Galerkin method for the advection–
diffusion–reaction equations with fractional lower-order terms in one dimension. We first …

We propose a novel and simple spectral method based on the semi-discrete Fourier
transforms to discretize the fractional Laplacian (− Δ) α 2. Numerical analysis and …

For the fractional Laplacian of variable order, an efficient and accurate numerical evaluation
in multi-dimension is a challenge for the nature of a singular integral. We propose a simple …

In this article we show that the fractional Laplacian in $ R^{2} $ can be factored into a
product of the divergence operator, a Riesz potential operator, and the gradient operator …

We study numerical approximation for one-dimensional stochastic elliptic equations with
integral fractional Laplacian and the additive Gaussian noise of power-law: 1/f^β noise and …