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HIV, like many other infections, is a severe and lethal infection. Fractal-fractional operators are frequently used in modeling numerous physical processes in the current decade. These operators provide better dynamics of a mathematical model because these are the generalization of integer and fractional-order operators. This paper aims to study the dynamics of the HIV model during primary infection by fractal-fractional Atangana–Baleanu (AB) operators. The sufficient conditions for the existence and uniqueness of the solution of the proposed model under the AB operator are derived via fixed point theory. The numerical scheme is presented by using the Adams–Bashforth method. Numerical results are demonstrated for different fractal and fractional orders to see the effect of fractional order and fractal dimension on the dynamics of HIV and CD4+ T-cells during primary infection.

Study of HIV Disease and Its Association with Immune Cells under Nonsingular and Nonlocal Fractal-Fractional Operator