[1] Abbasi, Z., Izadi, M. and Hosseini, M.M. A highly accurate matrix method for solving a
class of strongly nonlinear BVP arising in modeling of human shape corneal, Math. Meth.
Appl. Sci. 46(2) (2023) 1511–1527.
[2] Alshammari, A.O., Ahmad, I., Jan, R. and Idris, S.A. Fractional-calculus analysis of the
dynamics of CD4+T cells and human immunodeficiency viruses, Eur. Phys. J. Spec. Top.
234(8) (2025) 1991–2003. https://doi.org/10.1140/epjs/s11734-024-01192-5
[3] Amin, R., YÜZBAŞI, Ş. and Nazir, S. Efficient numerical scheme for the solution of HIV
infection CD4+T-cells using Haar wavelet technique, Comput. Model. Eng. Sci. 131(2)(2022) 639–653. https://doi.org/10.32604/cmes.2022.019154.
[4] Arafa A.A.M., Rida S.Z., Khalil M., Fractional modeling dynamics of HIV and CD4+T-cells
during primary infection, Nonlinear Biomed. Phys. 6 (2012) 1–7.
[5] Arshad, S., Baleanu, D., Bu, W. and Tang, Y., Effects of HIV infection on CD4+T-cell
population based on a fractional-order model, Adv. Differ. Equ. 2017 (2017) 92. https:
//doi.org/10.1186/s13662-017-1143-0.
[6] Bajaria, S.H., Webb, G., Cloyd, M. and Kirschner, D. Dynamics of naive and memory
CD4+ T lymphocytes in HIV-1 disease progression, J. Acquir. Immune Defic. Syndr. 30(1)
(2002) 41–58.
[7] Baleanu, D., Diethelm, K., Scalas, E. and Trujillo J.J., Fractional Calculus Models and
Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, 2012.
https://doi.org/10.1142/8180.
[8] Hasani-Lichae, B., Biazar, J. and 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. 201 (1) (2019) 4059549. https://doi.org/10.1155/2019/4059549.
[9] Culshaw, R.V. and Ruan, S. A delay-differential equation model of HIV infection of CD4+T-
cells, Math. Biosci. 165 (2000) 27–39.
[10] Dinga, Y. and Yea, H., A fractional-order differential equation model of HIV infection of
CD4+T-cells, Math. Comput. Model. 50 (2009) 386–392.
[11] Diethelm, K. , The analysis of fractional differential equations, Springer, Berlin, 2010.
[12] Floater, M.S. and Hormann, K., Barycentric rational interpolation with no poles and high
rates of approximation, J. Numer. Math. 107 (2) (2007) 315–331.
[13] Fuda, C., Numerical stability of barycentric interpolation,Doctoral Dissertation submitted to
the Faculty of Informatics of the Università della Svizzera italiana, Doctoral Dissertation
submitted to the Faculty of Informatics of the Università della Svizzera italiana, 2024.
[14] Galperin, E.A., Kansa, E.J., Makroglou, A. and Nelson, S.A., Variable transformations in
the numerical solution of second kind Volterra integral equations with continuous and weakly
singular kernels; extensions to Fredholm integral equations, J. Comput. Appl. Math. 115 (1)
(2000) 193–211.
[15] Hernandez-Vargas, E.A. and Middleton, R.H. Modeling the three stages in HIV infection,
J. Theor. Biol. 7(320) (2013)33–40. doi:10.1016/J.JTBI.2012.11.028.
[16] Hilfer, R. (Ed.), Applications of fractional calculus in physics. World Scientific, Singapore,
2000.
[17] Katani, R. and McKee, S., A product integration method for nonlinear second kind Volterra
integral equations with a weakly singular kernel (with application to fractional differential
equations), Appl. Math. Lett. 163 (2025) 109403.
[18] Katani, R. and Shahmorad, S., A block by block method for solving system of Volterra integral
equations with continuous and Abel kernels, Math. Model. Anal. 20 (6) (2015), 737–753.
[19] Khader, M.M. The modeling dynamics of HIV and CD4+T-cells during primary infection
in fractional order: numerical simulation, Mediterr. J. Math. 15(3) (2018) 139. https:
//doi.org/10.1007/s00009-018-1178-9.
[20] Laurie, D.P., Periodizing transformations for numerical integration, J. Comp. Appl. Math.
66 (1-2)(1983) 337–344.
[21] Li, M. and Huang, C. The linear barycentric rational quadrature method for auto-convolution
Volterra integral equations. J. Sci. Comput. 78 (2019) 549–564. https://doi.org/10.1007/
s10915-018-0779-6.
[22] Liu, H., Ma, Y., Li, H. and Zhang, W., Combination of discrete technique on graded meshes
with barycentric rational interpolation for solving a class of time-dependent partial integro-
differential equations with weakly singular kernels, Comput. Math. Appl. 141 (2023) 159–169,
https://doi.org/10.1016/j.camwa.2023.04.018.
[23] Ma, J., A class of reducible quadrature rules for the second-kind Volterra integral equations
using barycentric rational interpolation, J. Comput. Appl. Math. 445 (2024) 115803. https:
//doi.org/10.1016/j.cam.2024.115803.
[24] McKee, S., Tang, T. and Diogo, T., An Euler-type method for two-dimensional Volterra
integral equations of the first kind. IMA J. Numer. Anal. 20(3) (2000) 423–440.
[25] O’Regan D., Agarwal R.P. and Perera K. ,Nonlinear integral equations singular in the
dependent variable, Appl. Math. Lett. 20 (2007) 1137-1141
[26] Parand, K., Kalantari, Z., Delkhosh, M., Quasilinearization-Lagrangian method to solve
the HIV infection model of CD4+T cells, SeMA 75 (2018) 271–283. https://doi.org/10.
1007/s40324-017-0133-1
[27] Perelson, A.S., Kirschner, D.E. and Boer, R. De, Dynamics of HIV infection of CD4C
T-cells, Math. Biosci. 114 (1993) 81–125.
[28] Podlubny, I., Fractional differential equations: An introduction to fractional derivatives,
fractional differential equations, to methods of their solution and some of their applications,
Elsevier, 1998.
[29] Salah, E.Y., Sontakke, B., Abdo, M.S., Shatanawi, W., Abodayeh, K., Albalwi, M.D.
and Kamrujjaman, Md., Conformable fractional-order modeling and analysis of HIV/AIDS
transmission dynamics, Int. J. Differ. Equ. 2024(1) (2024) 1958622.
[30] Sokhanvar, E. and Askari Hemmat, A., Numerical solution of a fractional model for HIV
infection of CD4+T cells via Legendre multiwavelet functions, Int. J. Bioautomation 24 (4)
(2020) 359–370. doi:10.7546/ijba.2020.24.4.000634.
[31] Yildirim, G. and Y¨uzbasi, S.,Numerical solutions of SIRD model of Covid-19 by utilizing
Pell-Lucascollocation method, Turk. J. Math. 48 (6) (2024) 1156–1182.https://doi.org/
10.55730/1300-0098.3567
[32] Y¨uzbasi, S., A numerical approach to solve the model for HIV infection of CD4+T cells,
Appl. Math. Model. 36 (2012) 5876–5890.
[33] Y¨uzbasi, S. and Izadi, M., Bessel-quasilinearization technique to solve the fractional-order
HIV-1 infection of CD4+T-cells considering the impact of antiviral drug treatment, Appl.
Math. Comput. 431 (2022) 127319. https://doi.org/10.1016/j.amc.2022.127319.
[34] Y¨uzbasi, S. and Karacayir, M., An exponential Galerkin method for solutions of HIV
infection model of CD4+T-cells Comput. Biol. Chem. 67(2017)205–212. DOI10.1016/j.
compbiolchem.2016.12.006
[35] Zhao, Z. and Huang, C. Collocation methods based on barycentric rational interpolation for
Volterra integro-differential equations with weakly singular kernels, Math. Methods Appl.
Sci. 48 (2023) 8007–8023. https://doi.org/10.1002/mma.9468
