On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative, By Ardashir Mohammadzadeh

Research

Title	On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative
Type	Article
Keywords	: Mathematical model of HIV/AIDS transmission; Fractal fractional derivative; Stability; α-ψ-Geraghty type contraction; Gegenbauer polynomials
Researchers	Yanru Wu، Monire Nosrati Sahlan، Hojat Afshari، Maryam Atapour، Ardashir Mohammadzadeh

Abstract

In this study, we explore a mathematical model of the transmission of HIV/AIDS. The model incorporates a fractal fractional order derivative with a power-law type kernel. We prove the existence and uniqueness of a solution for the model and establish the stability conditions by employing Banach’s contraction principle and a generalized α-ψ-Geraghty type contraction. We perform stability analysis based on the Ulam–Hyers concept. To calculate the approximate solution, we utilize Gegenbauer polynomials via the spectral collocation method. The presented model includes two fractal and fractional order derivatives. The influence of the fractional and fractal derivatives on the outbreak of HIV is investigated by utilizing real data from the Cape Verde Islands in 1987–2014