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, we shall review an approach by which we can seek higher order time
discretisation schemes for solving time fractional partial differential equations with …

We introduce a modified L1 scheme for solving time fractional partial differential equations
and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and …

In this paper, we investigate an efficient technique for solving fractional integro-differential
equations (FIDEs) that have numerous applications in various fields of science. The …

This paper is concerned with the construction and analysis of a novel linearized compact
ADI scheme for the two-dimensional Riesz space fractional nonlinear reaction–diffusion …

We design and analyze several finite element methods (FEMs) applied to the Caffarelli–
Silvestre extension that localizes the fractional powers of symmetric, coercive, linear elliptic …

Abstract Gao et al.[11](2014) introduced a numerical scheme to approximate the Caputo
fractional derivative with the convergence rate O (k 3− α), 0< α< 1 by directly approximating …

In this letter, a new reproducing kernel collocation method is presented for solving nonlocal
fractional boundary value problems with non-smooth solutions. The method is based on the …

An all-at-once system of nonlinear algebra equations arising from the nonlinear tempered
fractional diffusion equation with variable coefficients is studied. Firstly, both the nonlinear …

In this paper, an alternating direction implicit legendre spectral (ADILS) method is developed
for the two-dimensional (2D) multi-term time fractional Oldroyd-B fluid type diffusion …