In this review paper, we are mainly concerned with the finite difference methods, the
Galerkin finite element methods, and the spectral methods for fractional partial differential …

In this paper, we shall review an approach by which we can seek higher order time
discretisation schemes for solving time fractional partial differential equations with …

Starting with the asymptotic expansion of the error equation of the shifted Grünwald–
Letnikov formula, we derive a new modified weighted shifted Grünwald–Letnikov (WSGL) …

A unified fast time-step** method for both fractional integral and derivative operators is
proposed. The fractional operator is decomposed into a local part with memory …

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

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 …

This paper is primarily concern with the formulation and analysis of a reliable numerical
method based on the novel alternating direction implicit finite difference scheme for the …

In this paper, a new derived method is developed for a known numerical differential formula
of the Caputo fractional derivative of order γ ∈ (1, 2) γ∈(1, 2)(Li and Zeng in Numerical …

This paper focuses on the design and analysis of an efficient numerical method based on
the novel implicit finite difference scheme for the solution of the dynamics of reaction …

In this paper, a high-order local discontinuous Galerkin (LDG) method combined with
weighted and shifted Grünwald difference (WSGD) approximation is developed and …