University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 6 2 2015 10 01 A Nonstandard Finite Difference Scheme for Solving‎ ‎Fractional-order Model of HIV-1 Infection of‎ ‎CD4^{+} t-cells 169 184 10843 10.22052/ijmc.2015.10843 EN S. Zibaei Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran M. Namjoo Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran Journal Article 2014 11 24 ‎In this paper‎, ‎we introduce fractional-order into a model of HIV-1 infection of CD4^+ T--cells‎. ‎We study the effect of ‎the changing the average number of viral particles $N$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎The nonstandard finite difference (NSFD) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order HIV-1‎ ‎infection model.‎ ‎ ‎Numerical results show that the‎ ‎NSFD approach is easy to be implemented and accurated when applied to fractional-order HIV-1‎ ‎infection model. HIV-1 model‎ ‎Nonstandard finite difference scheme‎ ‎Fractional differential equations‎ ‎Grunwald-Letnikov derivative‎ ‎Stability https://ijmc.kashanu.ac.ir/article_10843_596181178c783132f395514fe2e6bb51.pdf