# Analytic study for a fractional model of HIV infection of $CD4^{+}T$ lymphocyte cells

Volume 2, Issue 1, pp 33--43 Publication Date: May 12, 2018       Article History
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### Authors

Hasan Bulut - Department of Mathematics, Faculty of Science, Firat University, Elazig, Turkey
Devendra Kumar - Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India
Jagdev Singh - Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India
Ram Swroop - Department of Mathematics, Arya Institute of Engineering \& Technology, Rajasthan, India
Haci Mehmet Baskonus - Department of Computer Engineering, Munzur University, Tunceli, Turkey

### Abstract

In this article, we implemented homotopy transform methods, namely, homotopy analysis transform method and homotopy perturbation Sumudu transform method to examine the fractional model for HIV infection of $CD4^{+} T$ lymphocyte cells. Proliferation of $CD4^{+} T$ lymphocyte cells is driven by a combination of the homeostatic response to cells depletion ($CD4^{+} T$ cells counts) and viral load (HIV levels). The attraction of both the methods is that an approach of HPSTM is used and on other hand by HATM a large admissible convergence range of series solution is described for standard as well as fractional order nonlinear problems.

### Keywords

• Homotopy perturbation Sumudu transform method
• Laplace transform method
• Homotopy analysis transform method
• fractional model for HIV infection of $CD4^{+}T$ lymphocyte cells
• $\hbar$-curves

•  34A08
•  35A20
•  35A22