For the first time in literature, semi-implicit spectral approximations for nonlinear Caputo time-
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …

A survey is given of convergence results that have been proved when the L1 scheme is
used to approximate the Caputo time derivative Dα t (where 0< α< 1) in initial-boundary …

Starting with an introduction to fractional derivatives and numerical approximations, this
book presents finite difference methods for fractional differential equations, including time …

In this paper, we study the orthogonal Gauss collocation method (OGCM) with an arbitrary
polynomial degree for the numerical solution of a two-dimensional (2D) fourth-order …

In this paper, a fully-discrete alternating direction implicit (ADI) difference method is
proposed for solving three-dimensional (3D) fractional subdiffusion equations with variable …

In this paper, a new derived method is developed for a known numerical differential formula
of the Caputo fractional derivative of order γ ∈ (1, 2) γ∈(1, 2)(Li and Zeng in Numerical …

A time fractional initial boundary value problem of mixed parabolic–elliptic type is
considered. The domain of such problem is divided into two subdomains. A reaction …

In consideration of the initial singularity of the solution, a temporally second-order fast
compact difference scheme with unequal time-steps is presented and analyzed for …

The Black–Scholes (B–S) equation has been recently extended as a kind of tempered time-
fractional B–S equations, which becomes an interesting mathematical model in option …

In this paper, we propose a space-time finite element method for the distributed-order time
fractional reaction diffusion equations (DOTFRDEs). First, using the composite trapezoidal …