Abstract
In this paper, we have extended the model of HIV-1 infection to the fractional mathematical model using Caputo-Fabrizio and Atangana-Baleanu fractional derivative operators. A detailed proof for the existence and the uniqueness of the solution of fractional mathematical model of HIV-1 infection in Atangana-Baleanu sense is presented. Numerical approach is used to find and study the behavior of the solution of the stated model using different derivative operators, and the graphical comparison between the solutions obtained for the Caputo-Fabrizio and the Atangana-Baleanu operator is presented to see which fractional derivative operator is more efficient.
Highlights
HIV stands for the Human Immunodeficiency Virus
It is an imperative determinant for the need for opportunistic infection (OI) prophylaxis
CD4+ T cell count is determined from blood as a part of laboratory monitoring for HIV infection
Summary
HIV stands for the Human Immunodeficiency Virus. This virus attacks a person’s immune system. CD4+ T cell count is a measure of immune function in a patient with HIV. It is an imperative determinant for the need for opportunistic infection (OI) prophylaxis. We will consider the fractional mathematical model of HIV-1 infection in sense of Caputo-Fabrizio derivative operator [17] and Atangana-Baleanu derivative operator [18]. The numerical solutions are presented for the fractional mathematical model in sense of the Caputo-Fabrizio and the Atangana-Baleanu derivative operator. Ζβt represents the Caputo-Fabrizio fractional derivative of order β and NðβÞ is a normalization function and the following holds Nð0Þ = Nð1Þ = 1: Definition 2 (see [19]). Let f be an integrable function on R, the fractional integral of Atangana-Baleanu fractional derivative of order β is given as
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
