10.1007/s40096-021-00450-0

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

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  • M. R. Doostdar1,
  • A. R. Vahidi*1,
  • T. Damercheli1,
  • E. Babolian2,
  1. Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, IR
  2. Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, 1561836314, IR

Published in Issue 2022-01-15

How to Cite

Doostdar, M. R., Vahidi, A. R., Damercheli, T., & Babolian, E. (2022). 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. Mathematical Sciences, 17(2 (June 2023). https://doi.org/10.1007/s40096-021-00450-0
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Abstract

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.

Keywords

  • Fractional calculus,
  • System of ordinary differential equations,
  • HIV infection,
  • Hybrid functions,
  • Legendre polynomials

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