Barycentric rational interpolation method for fractional-order differential equation model of HIV infection of CD4$^+$T-cells

In this work we study of HIV infection dynamics through fractional-order differential equations (FDEs) that gained significant attention due to its ability to model complex biological processes with greater accuracy. The fractional-order models provide a more flexible framework by incorporating memory effects and hereditary properties, which are crucial in understanding the progression of HIV infection in CD4+ T-cells. This paper introduces a novel numerical method for solving the FDE model of HIV infection by transforming the FDE system into a system of the weakly singular Volterra integral equation (SWSVIE) and applying a collocation method based on barycentric rational interpolation. A convergence analysis is given and estimated error is determined.This approach aims to enhance the accuracy and applicability of numerical solutions in modeling HIV dynamics which the numerical examples is provided to demonstrate the applicability and effectiveness of the proposed method.