A Study on Dynamics of CD4+ T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials

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