  This paper presents a new predictor-corrector numerical scheme suitable for
fractional differential equations. An improved explicit Atangana-Seda formula
is obtained by considering the neglected terms and used as the predictor stage
of the proposed method. Numerical formulas are presented that approximate the
classical first derivative as well as the Caputo, Caputo-Fabrizio and
Atangana-Baleanu fractional derivatives. Simulation results are used to assess
the approximation error of the new method for various differential equations.
In addition, a case study is considered where the proposed scheme is used to
obtained numerical solutions of the Gierer-Meinhardt activator-inhibitor model
with the aim of assessing the system's dynamics.
