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 generalize existing Jacobi--Gauss--Lobatto collocation methods for variable-order
fractional differential equations using a singular approximation basis in terms of weighted …

Starting with the asymptotic expansion of the error equation of the shifted Grünwald–
Letnikov formula, we derive a new modified weighted shifted Grünwald–Letnikov (WSGL) …

An open problem in the numerical analysis of spectral methods for fractional differential
equations is how to maintain the high-order accuracy for non-smooth solutions. The limited …

We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear
fractional differential equations with fractional order 0<β<1. From the known structure of the …

We develop spectral collocation methods for fractional differential equations with variable
order with two end-point singularities. Specifically, we derive three-term recurrence relations …

In this paper, the space-time Jacobi spectral collocation method (JSC Method) is used to
solve the time-fractional nonlinear Schr o¨ dinger equations subject to the appropriate initial …

In this work, a finite difference method of tunable accuracy for fractional differential equations
(FDEs) with end-point singularities is developed. Modified weighted shifted Grünwald …

Spectral and spectral element methods using Galerkin type formulations are efficient for
solving linear fractional PDEs (FPDEs) of constant order but are not efficient in solving …

Abstract The Gray–Scott (GS) model represents the dynamics and steady state pattern
formation in reaction–diffusion systems and has been extensively studied in the past. In this …