A novel L1-Predictor-Corrector method for the numerical solution of the generalized-Caputo type fractional differential equations

Abstract

This paper proposes a novel L1 -based predictor-corrector method for the fractional differential equations involving generalized-Caputo type derivative. A decomposition scheme is used to obtain the three-point predictor-corrector formula. The error and stability of the proposed method are given in detail. A computer virus and a five-dimensional Hopfield neural network models are solved using the proposed approach.