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 …

Recently, many models are formulated in terms of fractional derivatives, such as in control
processing, viscoelasticity, signal processing, and anomalous diffusion. In the present …

We develop the finite element method for the numerical resolution of the space and time
fractional Fokker–Planck equation, which is an effective tool for describing a process with …

In this paper, two finite difference/element approaches for the time-fractional subdiffusion
equation with Dirichlet boundary conditions are developed, in which the time direction is …

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 …

In this paper, we study the time–space fractional order (fractional for simplicity) nonlinear
subdiffusion and superdiffusion equations, which can relate the matter flux vector to …

This article aims to fill in the gap of the second-order accurate schemes for the time-
fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are …

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

The implicit finite difference scheme with the shifted Grünwald formula, which is
unconditionally stable, is employed to discretize fractional diffusion equations. The resulting …

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