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 …

In this paper, we consider a numerical method for the time-fractional diffusion equation. The
method uses a high order finite difference method to approximate the fractional derivative in …

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 present a new type of fractional operator, the Caputo–Katugampola
derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases …

The main aim of the current paper is to propose an efficient numerical technique for solving
two-dimensional space-multi-time fractional Bloch–Torrey equations. The current research …

The solution of fractional-order differential problems requires in the majority of cases the use
of some computational approach. In general, the numerical treatment of fractional differential …

In this paper, two numerical techniques are introduced to study numerically the general
fractional advertising model. This system describes the flux of the consumers from unaware …

In this article, based on the idea of combing symmetrical fractional centred difference
operator with compact technique, a series of even‐order numerical differential formulas …

A new high-order finite difference scheme to approximate the Caputo fractional derivative 1
2 (D t α 0 C f (tk)+ D t α 0 C f (tk− 1)), k= 1, 2,…, N, with the convergence order O (Δ t 4− α) …

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 …