In this review paper, we are mainly concerned with the numerical methods for solving
fractional equations, which are divided into the fractional differential equations (FDEs), time …

An improved constitutive model is proposed in which the time space upper-convected
derivative is used to characterize heat conduction phenomena. The space Riesz fractional …

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) …

In recent years, considerable attention has been devoted to distributed-order differential
equations mainly because they appear to be more effective for modelling complex …

In this paper, we investigate the finite volume method (FVM) for a distributed-order space-
fractional advection–diffusion (AD) equation. The mid-point quadrature rule is used to …

In this article, we apply the generalized BDF2-θ to the fractional mobile/immobile transport
equations for its temporal discretization and the finite element method in the spatial …

We develop a monotone finite volume method for the time fractional Fokker-Planck
equations and theoretically prove its unconditional stability. We show that the convergence …

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 …

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 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 …