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equations by He’s homotopy perturbation method Physics Letters A 366 (2007), 79-84. [5] SJ. Liao, An approximate solution technique not depending on small parameter: a special example.In J Nonlinear Mech 1995:30(3):371-80. [6] SJ. Liao, Boundary element method for general nonlinear differential operators. Eng Anal Boundary Element 1997; 20(2):91-9. [7] J.H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation 151 (2004) 287-292. [8] J. Biazar, M. Eslami, H. Ghazvini, Homotopy perturbation method for

., Sakthivel R., Homotopy perturbation technique for solving two-point boundary value problems–comparison with other methods , Comp. Physics Communications, 181, 2010, 1021–1024. [9] Hetmaniok E., Słota D., Wróbel A., Zielonka A., Application of the homotopy perturbation method for the systems of Volterra integral equations , Zesz. Nauk. PŚ, Mat. Stosow., 5, 2015, 71–77. [10] He J.H., Homotopy perturbation technique , Comput. Methods Appl. Mech. Eng., 178, 1999, 257 – 262. [11] Nayfeh A.H., Introduction to Perturbation Technique , John Wiley and Sons, New York 1981.

References A. M. Lyapunov, The General Problem of the Stability of Motion, Taylor & Francis, London, UK, 1992, English translation. J. H. He, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178 (1999), 257-262. N. H. Sweilam and M. M. Khader, Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method, Computers & Mathematics with Applications, 58 (2009), 2134-2141. J. Saberi-Nadjafi and A. Ghorbani, He's homotopy perturbation method: an effective tool for solving

using analytical/numerical methods. Many researchers have been working on various analytical methods for solving nonlinear oscillation systems in the last decades. Nowadays, the computational experience is significant, and several numerical methods have been suggested and analyzed under certain conditions. These numerical methods have been developed using different techniques such as Taylor series, homotopy perturbation method, quadrature formula, variation iteration method and decomposition method [ 1 , 2 , 3 , 4 , 5 , 6 , 7 ]. Noor et al. [ 8 ] have applied a

flow through a tapered artery with a stenosis . – Heat and Mass Transfer, vol.43, No.1, pp.69-94. [21] Misra J.C. and Adhikary S.D. (2016): MHD oscillatory channel flow, heat and mass transfer in a physiological fluid in presence of chemical reaction. – Alexandria Engineering Journal, vol.55, No.1, pp.287-297. [22] Mohyud-Din S.T. and Noor M.A. (2009): Homotopy perturbation method for solving partial differential equations. – Zeitschrift für Naturforschung A, vol.64, No.(3-4), pp.157-170. [23] Mekheimer K.S. and El Kot M.A. (2008): The micropolar fluid model for

References [1] F.B.M. Belgacem and R. Silambarasan, Theory of natural transform , Mathematics in Engineering, Science and Aerospace 3 (2012), no. 1, 105–135. [2] M.H. Cherif, K. Belghaba, and Dj. Ziane, Homotopy perturbation method for solving the fractional Fisher’s equation , International Journal of Analysis and Applications 10 (2016), no. 1, 9–16. [3] A.M. Elsheikh and T.M. Elzaki, Variation iteration method for solving porous medium equation , International Journal of Development Research 5 (2015), no. 6, 4677–4680. [4] P. Guo, The Adomian

sources or sinks. – Proceeding of the Indian Academy of Sciences, vol.88, No.4, pp.369-376. [22] Moalem D. (1976): Steady-state heat transfer within porous medium with temperature dependent heat generation. – International Journal of Heat and Mass Transfer, vol.19, pp.529-537. [23] Foraboschi F.P. and Federico I.Di. (1964): Heat transfer in Laminar flow of non-Newtonian heat generating fluids. – International Journal of Heat and Mass Transfer, vol.7, No.3, pp.315-318. [24] Jafar B. and Hossein A. (2009): Study of convergence of Homotopy Perturbation Method for

oscillators, Computer Methods in Applied Mechanics and Engineering, 196, 1133-1153. 5. Ghotbi A. R., Barari A. Ganji D. D. (2011), Solving ratio-dependent predator-prey system with constant effort harvesting using homotopy perturbation method, Mathematical Problems in Engineering, ID 945420. 6. He J. H. (1999), Variational iteration method: A kind of nonlinear analytical technique: Some examples, International Journal of Non- Linear Mechanics, 344, 699-708. 7. He J. H. (2004a), Comparison of homotopy perturbation method and homotopy analysis method, Appl. Math Comput., 156

REFERENCES [1] M. Dehghan, F. Shakeri, Solution of an integro-differential equation arising in oscillating magnetic fields using He’s homotopy perturbation method, Prog. Electromagn. Res., 78 (2008) 361–376. [2] A. M. Siddiqui, R. Mahmood, G.K. Ghori, Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder, Phys. Lett. A, 352 (2006) 404–410. [3] K. M. Tamizhmani, J. Satsuma, B. Grammaticos, V. Ramani, Nonlinear integro differential equations as a discreet systems, Inverse Probl., 15 (1999) 787–791. [4] L. Xu, J. H. He, Y

REFERENCES [1] ABDULAZIZ, O.—HASHIM, I.—MOMANI, S.: Solving systems of fractional differential equations by homotopy perturbation method , Phys. Lett. A. 372 (2008), no. 4, 451–459. [2] BOYD, J. P.: An analytical two-dimensional Bratu equation , J. Sci. Comput. 1 (1986), no. 2, 183–206. [3] BOYD, J. P.: Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation , Appl. Math. Comput. 142 (2003), 189–200. [4] EL-AJOU, A.—ABU ARQUB, O.—AL ZHOUR, Z.—MOMANI, S.: New