On the fractional-order model of HIV-1 infection of CD4⁺ T-cells under the influence of antiviral drug treatment

References

• Podlubny I. Fractional differential equations: applications. Vol. 198. San Diego: Academic Press Inc; 1999. p. 1–340.
   Google Scholar
• Baleanu D, Jajarmi A, Hajipour M. On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel. Nonlinear Dyn. 2018;94(1):397–414.
   Web of Science ®Google Scholar
• Mainardi F. Fractional calculus and waves in linear viscoelasticity. London: Imperrial College Press; 2014.
   Google Scholar
• Alsaedi A, Nieto JJ, Venktesh V. Fractional electrical circuits. Adv Mech Eng. 2015;7(12):1–7.
   Web of Science ®Google Scholar
• Khan U, Ellahi R, Khan R, et al. Extracting new solitary wave solutions of Benny-Luke equation and Phi-4 equation of fractional order by using (G'/G)-expansion method. Opt Quant Electron. 2017;49:362.
   Web of Science ®Google Scholar
• Rahmatullah ER, Mohyud-din ST, Khan U. Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method. Results in Physics. 2018;8:114–120.
   Web of Science ®Google Scholar
• Rocha D, Silva C J, Torres DFM. Stability and optimal control of a delayed HIV model. Math Methods Appl Sci. 2016;41(6):2251–2260.
   Web of Science ®Google Scholar
• Perelson AS, Ribeiro RM. Modeling the within-host dynamics of HIV infection. BMC Biol. 2013;11:96.
   PubMed Web of Science ®Google Scholar
• Wang S, Hottz P, Schechter M, et al. Modeling the slow CD4+ T cell decline in HIV-infected individuals. PLoS Comput Biol. 2015;11(12):1–25.
   Web of Science ®Google Scholar
• Weiss RA. How does HIV cause AIDS? Science. 1993;260:1273–1279.
   PubMed Web of Science ®Google Scholar
• Bonhoeffer S, Coffin JM, Nowak MA. Human immunodeficiency virus drug therapy and virus load. J Virol. 1997;71(4):3275–3278.
   Web of Science ®Google Scholar
• Tuckwell HC. Nature of equilibria and effects of drug treatments in some simple viral population dynamical models. Math Med Biol. 2000;17(4):311–327.
   Web of Science ®Google Scholar
• Arafa AAM, Rida SZ, Khalil M. The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional order model. Appl Math Model. 2013;37(4):2189–2196.
   Web of Science ®Google Scholar
• Pinto CMA, Carvalho ARM. A latency fractional order model for HIV dynamics. J Comput Appl Math. 2017;312:240–256.
   Web of Science ®Google Scholar
• Yan Y, Kou C. Stability analysis for a fractional differential model of HIV infection of CD4+ CD4+ T-cells with time delay. Math Comput Simul. 2012;82(9):1572–1585.
   Web of Science ®Google Scholar
• Ding Y, Ye H. A fractional-order differential equation model of HIV infection of CD4+ T-cells. Math Comput Model. 2009;50(3):386–392.
   Google Scholar
• Jajarmi A, Baleanu D. A new fractional analysis on the interaction of HIV with CD4 + T-cells. Chaos Solit Fractals. 2018;113:221–229.
   Web of Science ®Google Scholar
• Arafa AAM, Rida SZ, Khalil M. Fractional modeling dynamics of HIV and CD4 + T-cells during primary infection. Nonlinear Biomed Phys. 2012;6(1):1–7.
   PubMedGoogle Scholar
• Gandomani MR, Kajani MT. Numerical solution of a factional order model of HIV infection of CD4 + T cells using Müntz-Legendre polynomials. Int J Bioautomation. 2016;20(2):193–204.
   Google Scholar
• Rahman JU, Lu D, Hui YS, et al. Numerical investigation of fractional HIV model using Elzaki pojected differential transform method. Fractals. 2018;26(5):1850062.
   Web of Science ®Google Scholar
• Mohyud-Din ST, Yildirim A. Ma’s variation of parameters method for fisher’s equations. Adv Appl Math Mech. 2010;2(3):379–388.
   Web of Science ®Google Scholar
• Mohyud-Din ST, Ahmed N, Waheed A, et al. Solutions of fractional diffusion equations by variation of parameters method. Therm. Sci. 2015;19:69–75.
   Web of Science ®Google Scholar
• Mohyud-Din ST, Noor MA, Waheed A. Variation of parameters method for solving sixth-order boundary value problems. Commun Korean Math Soc. 2009;24(4):605–615.
   Google Scholar
• Molliq RY, Noorani MSM, Hashim I. Variational iteration method for fractional heat- and wave-like equations. Nonlinear Anal Real World Appl. 2009;10(3):1854–1869.
   Web of Science ®Google Scholar
• Odibat ZM, Momani S. Application of variational iteration method to nonlinear differential equations of fractional orde. Int J Nonlinear Sci Numer Simul. 2006;7(1):27–34.
   Web of Science ®Google Scholar
• Sontakke BR, Shelke AS, Shaikh AS. Solution of non-linear factional differential equations by variational iteration method and applications. Far East J Math Sci. 2019;110(1):113–129.
   Google Scholar
• Momani S, Odibat Z. Homotopy perturbation method for nonlinear partial differential equations of fractional order. Phys Lett A. 2007;365(5):345–350.
   Web of Science ®Google Scholar
• He JH. Homotopy perturbation technique. Comput Methods Appl Mech Eng. 1999;178(3):257–262.
   Web of Science ®Google Scholar
• Tripathi D. Numerical and analytical simulation of peristaltic flows of generalized Oldroyd-B fluids. Int J Numer Methods Fluids. 2011;67(12):1932–1943.
   Web of Science ®Google Scholar
• Tripathi D. Peristaltic transport of fractional Maxwell fluids in uniform tubes: applications in endoscopy. Comput Math Appl. 2011;62(3):1116–1126.
   Web of Science ®Google Scholar
• Tripathi D. Numerical study on peristaltic flow of generalized burgers’ fluids in uniform tubes in the presence of an endoscope. Int J Numer Meth Biomed Eng. 2011;27(11):1812–1828.
   Web of Science ®Google Scholar
• Abbas MA, Bai YQ, Bhatti MM, et al. Three dimensional peristaltic flow of hyperbolic tangent fluid in non-uniform channel having flexible walls. Alexandria Eng J. 2016;55(1):653–662.
   Web of Science ®Google Scholar
• Abdelsalam SI, Bhatti MM. The study of non-Newtonian nanofluid with hall and ion slip effects on peristaltically induced motion in a non-uniform channel. RSC Adv. 2018;8(15):7904–7915.
   PubMed Web of Science ®Google Scholar
• Abdelsalam SI, Bhatti MM. The impact of impinging TiO2 nanoparticles in Prandtl nanofluid along with endoscopic and variable magnetic field effects on peristaltic blood flow. Multidiscip Model Mater Struct. 2018;14(3):530–548.
   Web of Science ®Google Scholar
• Zeeshan A, Bhatti MM, Akbar NS, et al. Hydromagnetic blood flow of Sisko fluid in a non-uniform channel induced by peristaltic wave. Commun Theor Phys. 2017;68(1):103–110.
   Web of Science ®Google Scholar
• Shawagfeh NT. The decomposition method for fractional differential equations. J Fract Calc. 1999;16:27–33.
   Google Scholar
• Danesh M, Safari M. Application of adomian’s decomposition method for the analytical solution of space fractional diffusion equation. Adv Pure Math. 2011;1(6):345–350.
   Google Scholar
• Bakkyaraj T, Sahadevan R. An approximate solution to some classes of fractional nonlinear partial differential using adomian decomposition method. J Fract Calc Appl. 2014;5(1):37–52.
   Google Scholar
• Adomian G. Solving frontier problems of physics: the decomposition method. Amsterdam: Springer Netherlands; 1994.
   Google Scholar
• Beg OA, Tripathi D, Sochi T, et al. Adomian decomposition method (ADM) simulation of magneto-bio-tribological squeeze film with magnetic induction effects. J Mech Med Biol. 2015;15(5):1550072.
   Web of Science ®Google Scholar
• Shah K, Tunç C. Existence theory and stability analysis to a system of boundary value problem. J Taibah Univ Sci. 2017;11(6):1330–1342.
   Web of Science ®Google Scholar
• Tunç C, Tunç O. Qualitative analysis for a variable delay system of differential equations of second order. J Taibah Univ Sci. 2019;13(1):468–477.
   Web of Science ®Google Scholar
• Ellahi R, Hussain F, Ishtiaq F, et al. Peristaltic transport of Jeffrey fluid in a rectangular duct through a porous medium under the effect of partial slip: an approach to upgrade industrial sieves/filters. Pramana – J Phys. 2019;93:34.
   Web of Science ®Google Scholar
• Zeeshan A, Shehzad N, Abbas T, et al. Effects of radiative electro-magnetohydrodynamics diminishing internal energy of pressure-driven flow of titanium dioxide-water nanofluid due to entropy generation. Entropy. 2019;21:36.
   Web of Science ®Google Scholar
• Sohail A, Maqbool K, Ellahi R. On space spectral time fractional adam bashforth moulton method along with stability analysis for fractional order partial differential equations. Numer Methods Partial Differ Equ. 2018;34(1):19–29.
   Web of Science ®Google Scholar
• Sarafraz MM, Pourmehran O, Yang B, et al. Pool boiling heat transfer characteristics of iron oxide nano-suspension under constant magnetic field. Int J Therm Sci. 2020;147:106131.
   Web of Science ®Google Scholar
• Ellahi R, Sait SM, Shehzad N, et al. Numerical simulation and mathematical modeling of electroosmotic Couette-Poiseuille flow of MHD power-law nanofluid with entropy generation. Symmetry (Basel). 2019;11(8):1038.
   Google Scholar
• Alamri SZ, Khan AA, Azeez M, et al. Effects of mass transfer on MHD second grade fluid towards stretching cylinder: A novel perspective of Cattaneo–christov heat flux model. Phys Lett A. 2019;383:276–281.
   Web of Science ®Google Scholar
• Alamri SZ, Ellahi R, Shehzad N, et al. Convective radiative plane Poiseuille flow of nanofluid through porous medium with slip: An application of Stefan blowing. J Mol Liq. 2019;273:292–304.
   Web of Science ®Google Scholar
• Ellahi R, Alamri SZ, Basit A, et al. Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation. J Taibah Univ Sci. 2018;12(4):476–482.
   Web of Science ®Google Scholar
• Lichae BH, Biazar J, Ayati Z. The fractional differential model of HIV-1 infection of CD4 + T-cells with description of the effect of antiviral drug treatment. Comput Math Methods Med. 2019;2019:4059549.
   Web of Science ®Google Scholar
• Caputo M. Linear models of dssipation whose Q is almost frequency independent-II. Geophys. J. R. Astron. Soc. 1967;13(5):529–539.
   Web of Science ®Google Scholar
• Tuckwell HC, Wan FYM. On the behavior of solutions in viral dynamical models. BioSystems. 2004;73(3):157–161.
   Web of Science ®Google Scholar