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 …

The computational work and storage of numerically solving the time fractional PDEs are
generally huge for the traditional direct methods since they require total memory and work …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the
two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed …

This paper is concerned with numerical solutions of time-fractional nonlinear parabolic
problems by a class of $ L1 $-Galerkin finite element methods. The analysis of $ L1 …

In this paper, we consider spectral approximation of fractional differential equations (FDEs).
A main ingredient of our approach is to define a new class of generalized Jacobi functions …

Fractional partial order diffusion equations are a generalization of classical partial
differential equations, used to model anomalous diffusion phenomena. When using the …

The fractional derivatives include nonlocal information and thus their calculation requires
huge storage and computational cost for long time simulations. We present an efficient and …

In this article, a class of two-dimensional Riesz space fractional diffusion equations is
considered. Some fractional spaces are established and some equivalences between …

A new fourth-order difference approximation is derived for the space fractional derivatives by
using the weighted average of the shifted Grünwald formulae combining the compact …