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Abstract
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In recent decades, AIDS has been one of the main challenges facing the medical community
around the world. Due to the large human deaths of this disease, researchers have tried to study the
dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition
to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD4+
T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional
structure for the first time. The kernel of these new fractal-fractional operators is of the generalized
Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence
theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is
reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical
algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton
polynomials method. We simulate our results via these two algorithms and compare both of them. The
numerical results reveal some stability and a situation of lacking a visible order in the early days of the
disease dynamics when one uses the Newton polynomial.
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