In this paper, finite difference schemes for solving time-space fractional diffusion equations
in one dimension and two dimensions are proposed. The temporal derivative is in the …

This study aims to investigate some theoretical results, numerical study and a real-word
application of the SFGLE, involving the fractional Laplacian. First, we describe the …

In this paper, we investigate the numerical solution of the two-dimensional fractional
Laplacian wave equations. After splitting out the Riesz fractional derivatives from the …

In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schrödinger
equation (fNLSE) for the construction and analysis of its soliton solutions. We also …

Fundamental properties for the coefficients of a second-order finite difference approximation
of the fractional Laplacian in d≥ 2 dimensions are derived in this paper. The obtained decay …

In this paper, the (2+ 1)-dimensional nonlinear Schrödinger equation (2D NLSE) abreast of
the (2+ 1)-dimensional linear time-dependent Schrödinger equation (2D TDSE) are …

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 …

This paper studies numerical methods for the two-dimensional fractional Gray-Scott (GS)
model with fractional Laplacian. A three-level linearized difference scheme for solving the …

In this article, numerical algorithms are derived for ultra-slow (or superslow) diffusion
equations in one and two space dimensions, where the ultra-slow diffusion is characterized …

The Schrödinger equation with variable-order fractional operator is a challenging problem to
be solved numerically. In this study, an implicit fully discrete continuous Galerkin finite …