Abstract
This paper introduces fractional-order into a mathematical model of HIV infection of CD4$ ^{+} $ T-cells combining with the rate of multiply uninfected CD4$ ^{+} $ T-cells through mitosis and stem cell therapy. The paper shows the theoretical studies including positivity and stability of the solution. In addition, the numerical solutions are obtained and illustrated. The results show that the stem cell's therapy increases the quality of a HIV patient's life only for short time. This results are consistent with medical case studies.
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