In this paper, the two-dimensional distributed order space-fractional diffusion equation on an
irregular convex domain is considered. The finite element method using unstructured mesh …

This paper is concerned with the construction and analysis of a novel linearized compact
ADI scheme for the two-dimensional Riesz space fractional nonlinear reaction–diffusion …

In this article, a fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme,
which aims at solving nonlinear problems quickly, is considered to numerically solve the …

Most existing research on applying the finite element method to discretize space fractional
operators is studied on regular domains using either uniform structured triangular meshes …

In this paper, we study the time-fractional Euler–Poisson–Darboux equation with the Bessel
fractional derivative. The Laplacian operator of this equation is considered in the ordinary …

In this article, a new time two-mesh (TT-M) finite element (FE) method, which is constructed
by a new TT-M algorithm and FE method in space, is proposed and analyzed. The numerical …

In this paper, the two-dimensional multi-term time-space fractional diffusion-wave equation
on an irregular convex domain is considered as a much more general case for wider …

In this paper, we consider the numerical solutions of the semilinear Riesz space-fractional
diffusion equations (RSFDEs) with time delay, which constitute an important class of …

This article studies a direct numerical approach for fractional advection–diffusion equations
(ADEs). Using a set of cubic trigonometric B-splines as test functions, a differential …

To achieve the efficient and accurate long-time integration, we propose a fast and stable
high-order numerical method for solving fractional-in-space reaction–diffusion equations …