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 …

We establish the well-posedness of an hp-version time-stepping discontinuous Galerkin
method for the numerical solution of fractional superdiffusion evolution problems. In …

Time-stepping hp hp-versions discontinuous Galerkin (DG) methods for the numerical
solution of fractional subdiffusion problems of order-α-α with-1< α< 0-1< α< 0 will be …

We present an hp version of the continuous Petrov--Galerkin (CPG) finite element method
for linear Volterra integro-differential equations with smooth and nonsmooth kernels. We …

This paper discusses the upwinded local discontinuous Galerkin methods for the one-
term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice …

In this paper, we present an $ hp $-version Legendre-Jacobi spectral collocation method for
Volterra integro-differential equations with smooth and weakly singular kernels. We …

In this paper, a discontinuous Galerkin (DG) time stepping method combined with the
standard finite element method in space is proposed to solve a class of semilinear parabolic …

In this paper, several two-grid finite element algorithms for solving parabolic integro-
differential equations (PIDEs) with nonlinear memory are presented. Analysis of these …

We develop and analyze an hp-version of the discontinuous Galerkin time-stepping method
for linear Volterra integral equations with weakly singular kernels. We derive a priori error …

High-order adaptive methods for fractional differential equations are proposed. The methods
rely on a kernel compression scheme for the approximation and localization of the history …