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

A Newton interpolation based predictor-corrector numerical method for fractional differential equations with an activator-inhibitor case study