Fractal-Fractional HIV Dynamics with Mittag-Leffler Kernel: Analysis, Stability, and Numerical Simulations

In this paper, a fractal--fractional HIV model with the Mittag--Leffler kernel is proposed using the Atangana--Baleanu--Caputo operator to capture the memory and hereditary properties of the disease dynamics.

The existence and uniqueness of the solutions are investigated using suitable analytical techniques, and the Hyers--Ulam stability analysis is carried out to verify the stability behavior of the proposed system.

For the numerical simulations, the Newton polynomial approximation method together with the Atangana--Toufik numerical scheme is employed to obtain approximate solutions for different parameter settings.

Furthermore, several visualization techniques, including sensitivity heatmap representation and tornado diagram analysis, are utilized to study the influence of model parameters on the HIV dynamics.

The obtained numerical results demonstrate that the proposed fractal--fractional framework provides an effective and reliable approach for analyzing the transient and long-term behavior of HIV transmission dynamics.