OICC Press Mathematical Sciences 2251-7456 17 2 (June 2023) 2022 01 15 A numerical method based on hybrid functions for solving a fractional model of HIV infection of CD4+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document} T cells 10.1007/s40096-021-00450-0 EN M. R. Doostdar Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, IR A. R. Vahidi Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, IR T. Damercheli Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, IR E. Babolian Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, 1561836314, IR Journal Article 2022 01 15 Abstract In this work, we use a hybrid functions method for solving a fractional model for HIV infection of CD4 +\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document} T cells, which is described by a system of fractional ordinary differential equations (SFODEs) with quadratic nonlinearities. Here, the fractional derivatives are considered in the Caputo sense. By using this method, the selected system of FODEs is reduced to a system of algebraic equations. In convergence discussion of the method, an upper bound of the error is obtained. To show the efficiency and the applicability of the presented method, a numerical example is simulated, and the numerical results are compared with the reported results in the literature. Also, the effect of the order of fractional derivative on the numerical results is studied.