Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method

Abstract

In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models.