Parametrized predictor–corrector method for initial value problems with classical and Caputo–Fabrizio derivatives

Abstract

Ordinary 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.