Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …

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 …

Volterra partial integro-differential problems with weakly singular kernel attract a lot of
attentions in recent years, thanks to the numerous real world applications. Solving this kind …

In this paper, we propose a fast algorithm for the variable-order (VO) Caputo fractional
derivative based on a shifted binary block partition and uniform polynomial approximations …

In this article, neural network method (NNM) is presented to solve the spatiotemporal
variable-order fractional advection-diffusion equation with a nonlinear source term. The …

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 propose a fast block α-circulant preconditioner for solving the
nonsymmetric linear system arising from an all-at-once implicit discretization scheme in time …

Volterra subdiffusion problems with weakly singular kernel describe the dynamics of
subdiffusion processes well. The graded L 1 scheme is often chosen to discretize such …

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system
which arises from the time-fractional partial differential equation. Existing fast numerical …

In this paper, we present a fast (3-α)-order numerical method for the Caputo fractional
derivative based on the L2 scheme and the sum-of-exponentials (SOE) approximation to the …