A numerical method based on hybrid functions for solving a fractional model of HIV infection of CD4+ T cells

• Published in: Mathematical sciences (Karaj, Iran) Vol. 17; no. 2; pp. 157 - 167
• Main Authors: Doostdar, M. R., Vahidi, A. R., Damercheli, T., Babolian, E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus; Differential equations; HIV; Human immunodeficiency virus; Immune system; Infections; Lymphocytes; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Numerical analysis; Numerical methods; Ordinary differential equations; Original Research; Upper bounds; 33C45; 34A34; 26A33; System of ordinary differential equations; Hybrid functions; Legendre polynomials; HIV infection; Fractional calculus; 34A08
• ISSN: 2008-1359; 2251-7456
• DOI: 10.1007/s40096-021-00450-0

In this work, we use a hybrid functions method for solving a fractional model for HIV infection of CD4 + 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.