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

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 predictor stage of proposed method. Numerical formulas are presented that approximate classical first derivative well Caputo, Caputo–Fabrizio Atangana–Baleanu derivatives. Simulation results to assess approximation error method various In addition, case study considered where obtain solutions Gierer–Meinhardt activator–inhibitor model with aim assessing system’s dynamics.