| Summary: | In this paper, a mathematical model of generalized fractional-order is constructed to study the problem of human immunodeficiency virus (HIV) infection of CD$ 4^+ $ T-cells with treatment. The model consists of a system of four nonlinear differential equations under the generalized Caputo fractional derivative sense. The existence results for the fractional-order HIV model are investigated via Banach's and Leray-Schauder nonlinear alternative fixed point theorems. Further, we also established different types of Ulam's stability results for the proposed model. The effective numerical scheme so-called predictor-corrector algorithm has been employed to analyze the approximated solution and dynamical behavior of the model under consideration. It is worth noting that, unlike many discusses recently conducted, dimensional consistency has been taken into account during the fractionalization process of the classical model.
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