  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.
