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

The trajectory of fractional calculus has undergone several periods of intensive
development, both in pure and applied sciences. During the last few decades fractional …

The Fokker--Planck (FP) equation governing the evolution of the probability density function
(PDF) is applicable to many disciplines, but it requires specification of the coefficients for …

In this article, we will discuss the applications of the Spectral element method (SEM) and
Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element …

Since fractional derivatives are integrals with weakly singular kernel, the discretization on
the uniform mesh may lead to poor accuracy. The finite difference approximation of Caputo …

In this paper, a fast linearized conservative finite element method is studied for solving the
strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme …

Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can
not be modeled accurately by the second-order diffusion equations. Because of the nonlocal …

We investigate the time average mean-square displacement δ 2¯(x (t))=∫ 0 t− Δ [x (t′+ Δ)−
x (t′)] 2 dt′∕(t− Δ) for fractional Brownian-Langevin motion where x (t) is the stochastic …

We consider the initial boundary value problem for a homogeneous time-fractional diffusion
equation with an initial condition v(x) and a homogeneous Dirichlet boundary condition in a …