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 obtain numerical solutions of the Gierer–Meinhardt activator–inhibitor model with the aim of assessing the system’s dynamics.

本文提出了一种适用于分数阶微分方程的新的预测器-校正器数值方案。通过考虑被忽略的术语获得改进的显式Atangana–Seda公式，并将其用作所提出方法的预测阶段。提出了近似经典一阶导数以及Caputo，Caputo–Fabrizio和Atangana–Baleanu分数导数的数值公式。仿真结果用于评估新方法对各种微分方程的近似误差。此外，还考虑了一个案例研究，其中所提出的方案用于获得Gierer-Meinhardt活化剂-抑制剂模型的数值解，目的是评估系统的动力学。