This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
S. Abbasbandy and E. Shivanian, (2011). A new analytical technique to solve Fredholm’s integral equations, Numer. Algor. 56, 27–43.AbbasbandyS.ShivanianE.2011A new analytical technique to solve Fredholm’s integral equations56274310.1007/s11075-010-9372-2Search in Google Scholar
R. Brociek, E. Hetmaniok, J. Matlak, and D. Słota, (2016). Application of the homotopy analysis method for solving the systems of linear and nonlinear integral equations, Math. Model. Anal. 21, 350–370.BrociekR.HetmaniokE.MatlakJ.SłotaD.2016Application of the homotopy analysis method for solving the systems of linear and nonlinear integral equations2135037010.3846/13926292.2016.1167787Search in Google Scholar
D.S. Chauhan, R. Agrawal, and P. Rastogi, (2012). Magnetohydrodynamic slip flow and heat transfer in a porous medium over a stretching cylinder: homotopy analysis method, Numer. Heat Transfer A 62, 136–157.ChauhanD.S.AgrawalR.RastogiP.2012Magnetohydrodynamic slip flow and heat transfer in a porous medium over a stretching cylinder: homotopy analysis method62136157Search in Google Scholar
T. Fan and X. You, (2013). Optimal homotopy analysis method for nonlinear differential equations in the boundary leyer, Numer. Algor. 62, 337–354.FanT.YouX.2013Optimal homotopy analysis method for nonlinear differential equations in the boundary leyer6233735410.1007/s11075-012-9587-5Search in Google Scholar
H. Gliński, R. Grzymkowski, A. Kapusta, and D. Słota, (2012) Mathematica 8, WPKJS, Gliwice (in Polish).GlińskiH.GrzymkowskiR.KapustaA.SłotaD.2012WPKJSGliwicein PolishSearch in Google Scholar
K. Gromysz, (2013). Examination of the Reinforced Concrete Plates Loaded Temporarily, Periodicaly and Kinematically, Monograph no 452, Silesian University of Technology Press, Gliwice (in Polish).GromyszK.2013Silesian University of Technology PressGliwicein PolishSearch in Google Scholar
E. Hetmaniok, I. Nowak, D. Słota, and R. Wituła, (2015). Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations, J. Numer. Math. 23, 331–344.HetmaniokE.NowakI.SłotaD.WitułaR.2015Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations2333134410.1515/jnma-2015-0022Search in Google Scholar
E. Hetmaniok, D. Słota, T. Trawiński, and R. Wituła, (2014). Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind, Numer. Algor. 67, 163–185.HetmaniokE.SłotaD.TrawińskiT.WitułaR.2014Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind6716318510.1007/s11075-013-9781-0Search in Google Scholar
E. Hetmaniok, D. Słota, R. Wituła, and A. Zielonka, (2015). An analytical method for solving the two-phase inverse Stefan problem, Bull. Pol. Ac.: Tech 63(3), 583–590.HetmaniokE.SłotaD.WitułaR.ZielonkaA.2015An analytical method for solving the two-phase inverse Stefan problem63358359010.1515/bpasts-2015-0068Search in Google Scholar
E. Hetmaniok, D. Słota, R. Wituła, and A. Zielonka, (2015). Solution of the one-phase inverse Stefan problem by using the homotopy analysis method, Appl. Math. Modelling 39, 6793–6805.HetmaniokE.SłotaD.WitułaR.ZielonkaA.2015Solution of the one-phase inverse Stefan problem by using the homotopy analysis method396793680510.1016/j.apm.2015.02.025Search in Google Scholar
T. Kaczorek, (2016). A new approach to the realization problem for fractional discrete-time linear systems, Bull. Pol. Ac.: Tech 64(1), 9–14.KaczorekT.2016A new approach to the realization problem for fractional discrete-time linear systems64191410.1515/bpasts-2016-0002Search in Google Scholar
Y. Khan, M. Fardi, (2015). A new efficient multi-parametric homotopy approach for two-dimensional Fredholm integral equations of the second kind, Hacettepe J. Math. Stat. 44, 93–99.KhanY.FardiM.2015A new efficient multi-parametric homotopy approach for two-dimensional Fredholm integral equations of the second kind44939910.15672/HJMS.2015449096Search in Google Scholar
Y. Khan, K. Sayevand, M. Fardi, M. Ghasemi, (2014). A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equations, Appl. Math. Comput. 249, 229–236.KhanY.SayevandK.FardiM.GhasemiM.2014A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equations24922923610.1016/j.amc.2014.10.070Search in Google Scholar
R. Lewandowski, (2006). Dynamics of the Building Structures, Poznań University of Technology Press, Poznań 2006 (in Polish).LewandowskiR.2006Poznań University of Technology PressPoznań2006 (in Polish)Search in Google Scholar
S. Liao, (1998). Homotopy analysis method: a new analytic method for nonlinear problems, Appl. Math. Mech. – Engl. Ed. 19, 957–962.LiaoS.1998Homotopy analysis method: a new analytic method for nonlinear problems1995796210.1007/BF02457955Search in Google Scholar
S. Liao, (2003). Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman and Hall–CRC Press, Boca Raton.LiaoS.2003Chapman and Hall–CRC PressBoca Raton10.1201/9780203491164Search in Google Scholar
S. Liao, (2009). Notes on the homotopy analysis method: some definitions and theorems, Commun. Nonlinear Sci. Numer. Simulat. 14, 983–997.LiaoS.2009Notes on the homotopy analysis method: some definitions and theorems1498399710.1016/j.cnsns.2008.04.013Search in Google Scholar
S. Liao, (2010). An optimal homotopy-analysis approach for strongly nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simulat. 15, 2003–2015.LiaoS.2010An optimal homotopy-analysis approach for strongly nonlinear differential equations152003201510.1016/j.cnsns.2009.09.002Search in Google Scholar
S. Liao, (2012). Homotopy Analysis Method in Nonlinear Differential Equations, Springer/Higher Education Press, Berlin/Beijing.LiaoS.2012Springer/Higher Education PressBerlin/Beijing10.1007/978-3-642-25132-0Search in Google Scholar
Z.M. Odibat, (2010). A study on the convergence of homotopy analysis method, Appl. Math. Comput. 217, 782–789.OdibatZ.M.2010A study on the convergence of homotopy analysis method21778278910.1016/j.amc.2010.06.017Search in Google Scholar
P. Ostalczyk, (2015). On simplified forms of the fractional-order backward difference and related fractional-order linear discrete-time system description, Bull. Pol. Ac.: Tech 63(2), 423–433.OstalczykP.2015On simplified forms of the fractional-order backward difference and related fractional-order linear discrete-time system description63242343310.1515/bpasts-2015-0048Search in Google Scholar
M. Russo and R.A. Van Gorder, (2013). Control of error in the homotopy analysis of nonlinear Klein-Gordon initial value problems, Appl. Math. Comput. 219, 6494–6509.RussoM.Van GorderR.A.2013Control of error in the homotopy analysis of nonlinear Klein-Gordon initial value problems2196494650910.1016/j.amc.2012.12.049Search in Google Scholar
D. Słota, (2011). Homotopy Analysis Method and the Examples of Its Applications, Wyd. Pol. Śl., Gliwice (in Polish).SłotaD.2011Wyd. Pol. Śl.Gliwicein PolishSearch in Google Scholar
W. Sumelka, (2016). Fractional calculus for continuum mechanics – anisotropic non-locality, Bull. Pol. Ac.: Tech 64 (2), 361–372.SumelkaW.2016Fractional calculus for continuum mechanics – anisotropic non-locality64236137210.1515/bpasts-2016-0041Search in Google Scholar
M. Turkyilmazoglu, (2010). A note on the homotopy analysis method, Appl. Math. Lett. 23, 1226–1230.TurkyilmazogluM.2010A note on the homotopy analysis method231226123010.1016/j.aml.2010.06.003Search in Google Scholar
M. Turkyilmazoglu, (2010). Convergence of the homotopy analysis method, arXiv, 1006.4460v1.TurkyilmazogluM.2010arXiv, 1006.4460v1Search in Google Scholar
K. Vajravelu, R.A. Van Gorder, (2012). Nonlinear Flow Phenomena and Homotopy Analysis. Fluid Flow and Heat Transfer, Springer/Higher Education Press, Berlin/Beijing.VajraveluK.Van GorderR.A.2012Springer/Higher Education PressBerlin/Beijing10.1007/978-3-642-32102-3Search in Google Scholar
R.A. Van Gorder, (2012). Control of error in the homotopy analysis of semi-linear elliptic boundary value problems, Numer. Algor. 61, 613–629.Van GorderR.A.2012Control of error in the homotopy analysis of semi-linear elliptic boundary value problems6161362910.1007/s11075-012-9554-1Search in Google Scholar
R.A. Van Gorder and K. Vajravelu, (2009). On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach, Commun. Nonlinear Sci. Numer. Simulat. 14, 4078–4089.Van GorderR.A.VajraveluK.2009On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach144078408910.1016/j.cnsns.2009.03.008Search in Google Scholar
X. Zhang, B. Tang, and Y. He, (2011). Homotopy analysis method for higher-order fractional integrodifferential equations, Comput. Math. Appl. 62, 3194–3203.ZhangX.TangB.HeY.2011Homotopy analysis method for higher-order fractional integrodifferential equations623194320310.1016/j.camwa.2011.08.032Search in Google Scholar
M. Zurigat, S. Momani, Z. Odibat, and A. Alawneh, (2010). The homotopy analysis method for handling systems of fractional differential equations, Appl. Math. Modelling 34, 24–35.ZurigatM.MomaniS.OdibatZ.AlawnehA.2010The homotopy analysis method for handling systems of fractional differential equations34243510.1016/j.apm.2009.03.024Search in Google Scholar