## Bessel-quasilinearization technique to solve the fractional-order HIV-1 infection of CD4+ T-cells considering the impact of antiviral drug treatment

Applied Mathematics and Computation, vol.431, 2022 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 431
• Publication Date: 2022
• Doi Number: 10.1016/j.amc.2022.127319
• Journal Name:
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
• Keywords: Bessel polynomials, Caputo's fractional derivative, Collocation points, Error and convergence analysis, Fractional-order HIV-1 infection model of CD4+ T-cells, Nonlinear differential equations, The technique of quasilinearization
• Akdeniz University Affiliated: Yes

#### Abstract

© 2022 Elsevier Inc.In this paper, two numerical methods based on the novel Bessel polynomials are developed to solve the fractional-order HIV-1 infection model of CD4+ T-cells considering the impact of antiviral drug treatment. In first of these methods, by using the Bessel polynomial and collocation points, we transform the HIV problem into a system of nonlinear algebraic equations. And this method, which is the method of direct solution is called as Bessel matrix method. The second method, which is called the Bessel-QLM method converts firstly HIV problem to a sequence of linear equations by using the technique of quasilinearization and then the reduced problem is solved by the direct Bessel matrix method. Error and convergence analysis are studied for the Bessel method. Finally, the applications are made on the numerical examples and also the numerical results are compared with the results of other available techniques. It is observed from applications that the presented results are better than the results of other existing methods and also the Bessel-QLM method is more efficient than the direct Bessel method.