On the formulation of a predictor–corrector method to model IVPs with variable‐order Liouville–Caputo‐type derivatives

Abstract

Variable‐order fractional calculus operators can be used as a valuable tool to simulate many nonlinear models with a memory property in fractional calculus applications. In this paper, we developed a novel predictor–corrector method for solving numerically nonlinear differential equations with variable‐order Liouville–Caputo‐type fractional derivatives. First, we found an inversion integral formula that is equivalent to the studied problem, and then we used it to formulate our numerical algorithm. Numerical approximate solutions of some variable‐order fractional models have been presented to display the efficiency and accuracy of the proposed algorithm. The influence of the variable‐order on the dynamic behavior of the considered problems is described.