Analysis of the Fractional HIV Model under Proportional Hadamard-Caputo Operators

Abstract

Modeling human immunodeficiency virus (HIV) via fractional operators has several benefits over the classical integer-order HIV model. The reason is that the fractional HIV model relies not only on the recent status but also on the former conduct of the model. Thus, we are motivated to introduce and analyze a new fractional HIV model. This article focuses on a novel fractional HIV model under the proportional Hadamard-Caputo fractional operators. The study of this model involves the existence and uniqueness (EU) of its solution and the stability examination. We employ Leray–Schauder nonlinear alternative (L-SNLA) and Banach’s fixed point theorems to analyze the EU results. In addition, for this provided model, we develop several forms of Ulam’s stability findings. As a special case of our results, we give and analyze a new fractional HIV model with Hadamard-Caputo operators. Moreover, by appropriate choice of the fractional parameters, the obtained outcomes are valid for analysis of the fractional HIV models formed by several fractional operators defined in the past literature.