Dynamical behaviour of HIV/AIDS model using Fractional Derivative with Mittag-Leffler Kernel

A mathematical model describing the HIV/AIDS transmission dynamics in the existence of an aware community using fractional differential operator having Mittag–Leffler kernel is presented and investigated in this paper. By using the fixed point theorem, the existence and uniqueness conditions of the model are obtained. We have used a novel technique known as the iterative Laplace transform approach to obtain the approximate solution of the mathematical model of HIV/AIDS based on the Atagana-Baleanu operator.We investigate the necessary conditions for the disease control in order to determine the role of unaware infective in the spread of HIV/AIDS. The numerical simulations and plots are demonstrated for different values of fractional order. Moreover, we have compared the obtained numerical results based on the Atagana-Baleanu operator with the values obtained using the Caputo operator for the suggested model. We believe that Atangana-Baleanue fractional derivative and the suggested algorithm are expected to be used in future to formulate and analyse many generalised fractional models.