[1] S. Abbasbandy, E. Shivanian, K. Vajravelu, Mathematical properties of h-curve in the frame work of the homotopy analysis method, Communications in Nonlinear Science and Numerical Simulation 16 (2011) 4268-4275.
[2] S. Abbasbandy, E. Magyari, E. Shivanian, The homotopy analysis method for multiple
solutions of nonlinear boundary value problems, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 3530-3536.
[3] S. Abbasbandy, E. Shivanian, Prediction of multiplicity of solutions of nonlinear boundary
value problems: novel application of homotopy analysis method, Communications in Nonlinear Science and Numerical Simulation 15 (2010) 3830-3846.
[4] S. Abbasbandy, E. Shivanian, Predictor homotopy analysis method and its application
tions in Nonlinear Science and Numerical Simulation 16 (2011) 2456-2468.
[5] S. Abbasbandy, E. Shivanian, A new analytical technique to solve Fredholm's integral equations, Numerical algorithms 56 (2011) 27-43.
[6] L. Ahmad Soltani, E. Shivanian, R. Ezzati, Convection-radiation heat transfer in solar heat exchangers lled with a porous medium: Exact and shooting homotopy analysis solution, Applied Thermal Engineering 103 (2016) 537-542.
[7] T. Allahviranloo, Z. Gouyandeh, A. Armand, Numerical solutions for fractional dierential equations by Tau-Collocation method, Applied Mathematics and Computation 271 (2015) 979-990.
[8] J. Biazar, M. A. Asadi, F. Salehi, Rational Homotopy Perturbation Method for solving sti systems of ordinary dierential equations, Applied Mathematical Modelling 39 (2015) 1291-1299.
[9] L. Bougoa, R. C. Rach, Solving nonlocal initial-boundary value problems for linear and nonlinear parabolic and hyperbolic partial dierential equations by the Adomian decomposition method, Applied Mathematics and Computation 225 (2013) 50-61.
[10] M. A. Fariborzi Araghi, S. Noeiaghdam, A novel technique based on the homotopy analysis
method to solve the rst kind Cauchy integral equations arising in the theory of airfoils, Journal of Interpolation and Approximation in Scientic Computing 2016 (2016) 1-13.
[11] M. A. Fariborzi Araghi, S. Noeiaghdam, Homotopy analysis transform method for solving generalized Abel's fuzzy integral equations of the rst kind, IEEE (2016). http://dx.doi.org/10.1109/CFIS.2015.7391645/
[12] M.A. Fariborzi Araghi, S. Noeiaghdam, Homotopy regularization method to solve the singular Volterra integral equations of the rst kind, Jordan Journal of Mathematics and Statistics (JJMS) 11 (2018) 1-12.
[13] M.A. Fariborzi Araghi, S. Noeighdam, Dynamical control of computations using the Gauss-Laguerre integration rule by applying the CADNA library, Advances and Applications in Mathematical Sciences 16 (2016) 1-18.
[14] M.A. Fariborzi Araghi, S. Noeiaghdam, A Valid Scheme to Evaluate Fuzzy Denite Integrals
by Applying the CADNA Library, International Journal of Fuzzy System Applications 6 (2017) 1-20. http://dx.doi.org/10.4018/IJFSA.2017100101/
[15] Sh. Gao, F. Zhang, Y. He, The eects of migratory bird population in a nonautonomous eco-epidemiological model, Applied Mathematical Modelling 37 (2013) 3903-3916.
[16] F. Geng, A modied variational iteration method for solving Riccati dierential equations,
Computers & Mathematics with Applications 60 (2010) 1868-1872.
[17] F. Geng, Y. Lin, M. Cui, A piecewise variational iteration method for Riccati dierential equations Open archive, Computers & Mathematics with Applications 58 (2009) 2518-2522.
[18] M. Ghoreishi, A.I.B.Md. Ismail, A.K. Alomari, Application of the homotopy analysis method for solving a model for HIV infection of CD4+ T-cells, Mathematical and Computer Modelling 54 (2011) 3007-3015.
[19] F. Guerrero, F.J. Santonja, R.J. Villanueva, Solving a model for the evolution of smoking
habit in Spain with homotopy analysis method, Nonlinear Analysis: Real World Applications 14 (2013) 549-558.
[20] Y. Hu, Y. Luo, Z. Lu, Analytical solution of the linear fractional dierential equation by Adomian decomposition method, Journal of Computational and Applied Mathematics 215 (2008) 220-229.
[21] K. Kamal Ali, H. Dutta, R. Yilmazer, S. Noeiaghdam, On the new wave behaviors of the Gilson-Pickering equation, Front. Phys. 8 (2012) 54-67.
[22] M. Khan, M.A. Gondal, I. Hussain, S. Karimi Vanani, A new comparative study between homotopy analysis transform method and homotopy perturbation transform method on a semi innite domain, Mathematical and Computer Modelling 55 (2012) 1143-1150.
[23] S. Kumar, D. Kumar, Fractional modelling for BBM-Burger equation by using new homotopy
analysis transform method, Journal of the Association of Arab Universities for Basic and Applied Sciences 16 (2014) 16-20.
[24] J. D. Lambert, Numerical Methods for Ordinary Dierential Systems: The Initial Value Problem, John Wiley and Sons, Chichester, UK, 1991.
[25] S. J. Liao, The proposed homotopy analysis techniques for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai, (1992) (in English).
[26] S. J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, (2003).
[27] S. J. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput. 147 (2004) 499-513.
[28] S.J. Liao, Homotopy analysis method in nonlinear dierential equations, Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg, 2012.
[29] K. Mallory, R. A. Van Gorder, Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation, Numerical Algorithms 64 (2013) 633-657.
[30] M. Mirzazadeh, Z. Ayati, New homotopy perturbation method for system of Burgers equations, Alexandria Engineering Journal 55 (2016) 1619-1624.
[31] P. M. Ngina, R. Waema Mbogo, L. S. Luboobi, Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the In uence of the CD8+ T-Cells, Applied Mathematics 8 (2017) 1153-1179.
[32] S. Noeiaghdam, A novel technique to solve the modied epidemiological model of computer viruses, SeMA Journal (2018). https://doi.org/10.1007/s40324-018-0163-3.
[33] S. Noeiaghdam, Numerical approximation of modied non-linear SIR model of computer
viruses, Contemporary Mathematics 1 (2019). http://dx.doi.org/10.37256/cm. 11201959.34-48/
[34] S. Noeiaghdam, E. Khoshrouye Ghiasi, Solving a non-linear model of HIV infection for CD4+T cells by combining Laplace transformation and Homotopy analysis method, arXiv:1809.06232.
[35] S. Noeiaghdam, E. Khoshrouye Ghiasi, An ecient method to solve the mathematical model of HIV infection for CD8+ T-cells. International Journal of Mathematical Modelling & Computations 9 (2019) 267-281.
[36] S. Noeiaghdam, M.A. Fariborzi Araghi, S. Abbasbandy, Finding optimal convergence control parameter in the homotopy analysis method to solve integral equations based on the stochastic arithmetic, Numer Algor 81 (2019) 237-267. http://dx.doi.org/10. 1007/s11075-018-0546-7/
[37] S. Noeiaghdam, M.A. Fariborzi Araghi, Finding optimal step of fuzzy Newton-Cotes integration rules by using the CESTAC method, Journal of Fuzzy Set Valued Analysis, 2017 (2017) 62-85. http://dx.doi.org/ 10.5899/2017/jfsva-00383/
[38] S. Noeiaghdam, D. Sidorov, I. Muftahov, A.V. Zhukov, Control of Accuracy on Taylor Collocation Method for Load Leveling Problem, The Bulletin of Irkutsk State University. Series Mathematics 30 (2019) 59-72. http://dx.doi.org/10.26516/1997-7670.2019.30.59/
[39] S. Noeiaghdam, D. Sidorov, V. Sizikov, N. Sidorov, Control of accuracy on Taylorcollocation
method to solve the weakly regular Volterra integral equations of the rst kind by using the CESTAC method, Applied and Computational Mathematics 19 (2020) 87-105.
[40] S. Noeiaghdam, M. Suleman, H. Budak, Solving a modied nonlinear epidemiological
model of computer viruses by homotopy analysis method, Mathematical Sciences 6 (2018) 1-12.
[41] S. Noeiaghdam, E. Zarei, H. Barzegar Kelishami, Homotopy analysis transform method for solving Abel's integral equations of the rst kind, Ain Shams Eng. J. 7 (2016) 483-495.
[42] M. Y. Ongun, The Laplace Adomian Decomposition Method for solving a model for HIV
infection of CD4+T cells, Mathematical and Computer Modelling 53 (2011) 597-603.
[43] Y. Ozturk, M. Gulsu, Numerical solution of a modied epidemiological model for computer
viruses, Applied Mathematical Modelling 39 (2015) 7600-7610.
[44] L. Pezza, F. Pitolli, A multiscale collocation method for fractional dierential problems, Mathematics and Computers in Simulation 147 (2018) 210-219.
[45] J.R. C. Piqueira, V. O. Araujo, A modied epidemiological model for computer viruses,
Applied Mathematics and Computation 213 (2009) 355-360.
[46] E. Shivanian, S. Abbasbandy, Predictor homotopy analysis method: two points second
order boundary value problems, Nonlinear Analysis: Real World Applications 15 (2014) 89-99.
[47] W. Sikander, U. Khan, N. Ahmed, S.T. Mohyud-Din, Optimal solutions for a bio mathematical model for the evolution of smoking habit, Results in Physics 7 (2017) 510-517.
[48] J. Singh, D. Kumar, Z. Hammouch, A. Atangana, A fractional epidemiological model for
computer viruses pertaining to a new fractional derivative, Applied Mathematics and Computation 316 (2018) 504-515.
[49] Y. Tan, S. Abbasbandy, Homotopy analysis method for quadratic Riccati dierential equation, Communications in Nonlinear Science and Numerical Simulation 13 (2008) 539-546.
[50] H. Thabet, S. Kendre, Analytical solutions for conformable space-time fractional partial
dierential equations via fractional dierential transform, Chaos, Solitons & Fractals 109 (2018) 238-245.
[51] E. Unal, A. Gokdogan, Solution of conformable fractional ordinary dierential equations via dierential transform method, Optik-International Journal for Light and Electron Optics 128 (2017) 264-273.
[52] R. A. Van Gorder, The variational iteration method is a special case of the homotopy analysis method, Applied Mathematics Letters 45 (2015) 81-85.
[53] H. Vazquez-Leal, F. Guerrero, Application of series method with Pade and Laplace-Pade resummation methods to solve a model for the evolution of smoking habit in Spain, Comp. Appl. Math. 33 (2014) 181-192.
[54] H. Xu, S.J. Liao, X.C. You, Analysis of nonlinear fractional partial dierential equations with the homotopy analysis method, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 1152-1156.
[55] L. Yakob, Endectocide-treated cattle for malaria control: A coupled ntomologicalepidemiological model, Parasite Epidemiology and Control 1 (2016) 2-9.
[56] S. Yuzbasi, A numerical approach to solve the model for HIV infection of CD4+T cells, Applied Mathematical Modelling 36 (2012) 5876-5890.