A New Caputo-Fabrizio Hybrid Method for the Numerical Solution of Caputo-Fabrizio Fractional Epidemic Model

Abstract

This paper presents a novel Caputo–Fabrizio hybrid numerical method for examining the dynamics of fractional epidemic models defined by memory effects and non-singular kernels. The proposed method combines the Caputo–Fabrizio fractional derivative with a hybrid transform framework, facilitating the derivation of accurate and convergent approximate solutions for nonlinear epidemic systems. The model's parameters are analyzed in relation to infection transmission and recovery dynamics, whereas the fractional order α regulates the magnitude of memory and genetic influences. Numerical simulations indicate that the novel hybrid method exhibits remarkable concordance with established results for integer-order scenarios, while showcasing enhanced precision, computing efficiency, and robustness in fractional contexts. The suggested method offers a versatile and effective analytical instrument for investigating real-world epidemic occurrences exhibiting long-term memory traits.