# Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations

## TL;DR

Neglecting the nonlocal properties of fractional differential operators results in unreliable numerical methods, as demonstrated by flaws in a recent approach that falsely claims high accuracy using local approximations.

## Contribution

This paper critically analyzes a recent numerical method for fractional differential equations, highlighting its neglect of nonlocality and exposing its inaccuracies.

## Key findings

- The method produces incorrect results due to ignoring nonlocality.
- Local-only schemes cannot reliably solve fractional differential equations.
- The paper warns against using similar flawed methods in future research.

## Abstract

In the paper titled "New numerical approach for fractional differential equations" by A. Atangana and K.M. Owolabi [Math. Model. Nat. Phenom., 13(1), 2018], it is presented a method for the numerical solution of some fractional differential equations. The numerical approximation is obtained by using just local information and the scheme does not present a memory term; moreover, it is claimed that third-order convergence is surprisingly obtained by simply using linear polynomial approximations. In this note we show that methods of this kind are not reliable and lead to completely wrong results since the nonlocal nature of fractional differential operators cannot be neglected. We illustrate the main weaknesses in the derivation and analysis of the method in order to warn other researchers and scientist to overlook this and other methods devised on similar basis and avoid their use for the numerical simulation of fractional differential equations.