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• [1] H.Kh. Abdullah, Oscillation conditions of second-order nonlinear differential equations, Int. J. Math. Sci. 34 (1), 1490-1497, 2014.
• [2] R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation theory for difference and differential equations, Kluwer academic publishers, Dordrecht, 2000.
• [3] R.P. Agarwal and D. O’Regan, An introduction to ordinary differential equations, Springer, Newyork, 2008.
• [4] B.C. Dhage and V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Anal. Hybrid Syst. 4, 414-424, 2010.
• [5] E.M. Elabbasy, T.S. Hassan and S.H. Saker, Oscillation of second-order nonlinear differential equations with a damping term, Electron. J. Differ. Eq. 76, 1-13, 2005.
• [6] X. Fu, T. Li and C. Zhang, Oscillation of second-order damped differential equations, Adv. Difference Equ. 326, 2013.
• [7] H. Ge and J. Xin, On the existence of a mild solution for impulsive hybrid fractional differential equations, Adv. Difference Equ. 211, 2013.
• [8] S.R. Grace, Oscillation theorems for nonlinear differential equations of second order, J. Math. Anal. Appl. 171, 220-241, 1992.
• [9] M.A.E. Herzallah and D. Baleanu, On fractional order hybrid differential equations, Abstr. Appl. Anal. 2014, Article ID 389386, 2014.
• [10] M. Heydari, G.B. Loghmani, S.M. Hosseini and S.M. Karbassi, Application of hybrid functions for solving diffing-harmonic oscillator, J. Difference Equ. 2014, Article ID 210754, 2014.
• [11] W.G. Kelley and A.C. Peterson, The theory of differential equations: classical and qualitative, Springer, NewYork, 2010.
• [12] H. Liu and F. Meng, Interval oscillation criteria for second-order nonlinear forced differential equations involving variable exponent, Adv. Difference Equ. 291, 2016.
• [13] Z. Luo and J. Shen, Oscillation of second order linear differential equations with impulses, Appl. Math. Lett. 20, 75-81, 2007.
• [14] K. Maleknejad and L. Torkzadeh, Application of hybrid functions for solving oscillator equations, Rom. Journ. Phys. 60 (1-2), 87-98, 2015.
• [15] J.V. Manojlovic, Oscillation criteria for second-order half-linear differential equations, Math. Comput. Modelling 30, 109-119, 1999.
• [16] P. Micheau and P. Coirault, A harmonic controller of engine speed oscillations for hybrid vehicles, Elsevier IFAC publications, 19-24, 2005.
• [17] A.K. Nandakumaran, P.S. Datti and R.K. George, Ordinary differential equations, principles and applications, Cambridge University Press, 2017.
• [18] A. Ozbekler, J.S.W. Wong, A. Safer, Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients, Appl. Math. Lett. 24, 1225-1230, 2011.
• [19] Ch.G. Philos, Oscillation theorems for linear differential equations of second order, Arch. Math. 53, 482-492, 1989.
• [20] V. Sadhasivam and M. Deepa, Oscillation criteria for fractional impulsive hybrid partial differential equations, Probl. Anal. Issues Anal. 8 (26), 73-91, 2019.
• [21] S.H. Saker, Oscillation theory of delay differential and difference equations, VDM Verlag, Dr.Muller Aktiengesellschaft and Co, USA, 2010.
• [22] S.H. Saker, P.Y.H. Pang and R.P. Agarwal, Oscillation theorems for second order nonlinear functional differential equations, Dynam. Systems Appl. 12, 307-322, 2003.
• [23] S. Sitho, S.K. Ntouyas and J. Tariboon, Existence results for hybrid fractional integrodifferential equations, Bound. Value Probl. 113, 1-13, 2015.
• [24] J.S.W. Wong, On Kamenev-type oscillation Theorems for second-order differential equations with damping, J. Math. Anal. Appl. 258, 244-257, 2001.
• [25] F. Yuan and D. DiClemente, Hybrid voltage-controlled oscillator with low phase noise andlarge frequency tunig range, Analog Integr Circ Sig Process 82, 471-478, 2015.
• [26] Y. Zhao, S. Sun, Z. Han and Q. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl. 62, 1312-1324, 2011.
• [27] A. Zhao, Y. Wang and J. Yan, Oscillation criteria for second-order nonlinear differential equations with nonlinear damping, Comput. Math. Appl. 56, 542-555, 2008.