Numerical Solution of Hybrid Fractional Differential Equations via Predictor-Corrector Method with Non-Singular Kernels

Abstract

This paper introduces a hybrid numerical method for fractional differential equations combining the Caputo-Fabrizio and Atangana Baleanu derivatives through a blending parameter. The resulting hybrid operator captures a spectrum of memory effects from exponential to power-law types, offering flexible and realistic modeling of complex systems. We develop a predictor-corrector scheme that efficiently approximates the resulting nonlinear integral equation, achieving second-order accuracy and stable convergence. The method’s effectiveness is demonstrated via a detailed fractional logistic growth example, showcasing smooth interpolation between memory behaviors and fast convergence. This approach broadens the toolbox for fractional calculus applications where multiple memory
scales coexist.