Atangana, AbdonAraz, Seda Igret2024-12-242024-12-2420240219-88781793-6977https://doi.org/10.1142/S0219887824400309https://hdl.handle.net/20.500.12604/7228Ordinary nonlinear differential equations with classical and fractional derivatives are used to simulate several real-world problems. Nonetheless, numerical approaches are used to acquire their solutions. While various have been proposed, they are susceptible to both disadvantages and advantages. In this paper, we propose a more accurate numerical system for solving nonlinear differential equations with classical and Caputo-Fabrizio derivatives by combining two concepts: the parametrized method and the predictor-corrector method. We gave theoretical analyses to demonstrate the method's correctness, as well as several illustrated examples for both scenarios.eninfo:eu-repo/semantics/closedAccessNonlinear ODEparametrized methodHeun's methodCaputo-Fabrizio derivativetheoretical analysisArticleN/AWOS:001275055800001Q22-s2.0-8519949116010.1142/S0219887824400309