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 …

Latterly, many problems arising in different fields of science and engineering can be
reduced, by applying some appropriate discretization, to a series of time-fractional partial …

In this paper, a spatial sixth-order numerical scheme for solving the time-fractional diffusion
equation (TFDE) is proposed. The convergence order of the constructed numerical scheme …

In this article, we present an efficient numerical algorithm, which combines the fourth-order
compact difference scheme (CDS) in space with the fast time two-mesh (TT-M) FBN-θ …

In this article, a nonlinear fractional Cable equation is solved by a two-grid algorithm
combined with finite element (FE) method. A temporal second-order fully discrete two-grid …

A new numerical scheme has been developed based on the fast and efficient meshless
local weak form ie direct meshless local Petrov–Galerkin (DMLPG) method for solving the …

Based on the price fluctuations of the underlying fractal transmission system, the α-order
time-fractional Black-Scholes model is obtained. In this paper, we introduce two compact …

In this article, a fully discrete local discontinuous Galerkin (LDG) method with high-order
temporal convergence rate is presented and developed to look for the numerical solution of …

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 …

The element free Galerkin technique is a meshless method based on the variational weak
form in which the test and trial functions are the shape functions of moving least squares …