In this review paper, we are mainly concerned with the numerical methods for solving
fractional equations, which are divided into the fractional differential equations (FDEs), time …

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) …

The usual classical polynomials-based spectral Galerkin and Petrov–Galerkin methods
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …

In this paper, we investigate the finite volume method (FVM) for a distributed-order space-
fractional advection–diffusion (AD) equation. The mid-point quadrature rule is used to …

In this article, a numerical method for solving a fractional-order Advection-Dispersion
equation (FADE) is proposed. The fractional-order derivative of the main problem is …

In recent years, non-Newtonian fluids have been widely applied in a number of engineering
applications. One particular subclass of non-Newtonian fluids is the generalized Oldroyd-B …

We apply two families of novel fractional θ θ-methods, the FBT-θ θ and FBN-θ θ methods
developed by the authors in previous work, to the fractional Cable model, in which the time …

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 …

In this article, a numerical scheme is formulated and analysed to solve the time-space
fractional advection–diffusion equation, where the Riesz derivative and the Caputo …

We develop a unified Petrov–Galerkin spectral method for a class of fractional partial
differential equations with two-sided derivatives and constant coefficients of the form D t 2 τ 0 …