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This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators., {"references":["T. Abdeljawad; On conformable fractional calculus, J. Comput. Appl.\nMath., 279, (2015), 57-66.","Mustafa Fahri Aktas¸; On the multivariate Lyapunov inequalities, Appl.\nMath. Comput. 232 (2014) 784-786.","Mustafa Fahri Aktas¸, Devrim C¸ akmak, Aydin Tiryaki; On Lyapunov type\ninequalities of a three-point boundary value problem for third order linear\ndifferential equations, Appl. Math. Lett., (2015), In Press.","Drumi Bainov, Valery Covachev; Impulsive Differential Equations With\na Small Parameter, World Scientific, (1994).","Sougata Dhar, Qingkai Kong; Liapunov-type inequalities for third-order\nhalf-linear equations and applications to boundary value problems,\nNonlinear Anal. Theory, Methods and Applications, 110 (2014), 170-181.","Rui A.C. Ferreira; A Lyapunov-type inequality for a fractional boundary\nvalue problem, Fract. Calc. Appl. Anal., Vol. 16, No 4 (2013), pp.\n978-984; DOI: 10.2478/s13540-013-0060-5.","Rui A. C. Ferreira; On a Lyapunov-type inequality and the zeros of\na certain Mittag-Leffler function, J. Math. Anal. Appl., 412, 2 (2014),\n1058-1063.","G. Sh. Guseinov, B. Kaymakc¸alan; Lyapunov inequalities for discrete\nlinear Hamiltonian systems, Comput. Math. Appl., 45, (2003), 1399-1416.","G. Sh. Guseinov, A. Zafer; Stability criterion for second order linear\nimpulsive differential equations with periodic coefficients, Math. Nachr.,\n281, No. 9, (2008), 1273-1282.\n[10] G. Sh. Guseinov, A. Zafer; Stability criteria for linear periodic impulsive\nHamiltonian systems, J. Math. Anal. Appl., 335, (2007), pp. 1195-1206.\n[11] Mohamad Jleli, Bessem Samet; Lyapunov type inequalities for a\nfractional differential equation with mixed boundary conditions, Math.\nInequal. Appl., Vol. 18, No. 2 (2015), 443-451.\n[12] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh; A new definition of\nfractional derivative, J. Comput. Appl. Math., 264, (2014), 65-70.\n[13] Xin-Ge Liu, Mei-Lan Tang; Lyapunov-type inequality for higher order\ndifference equations, Appl. Math. Comput. 232 (2014) 666-669.\n[14] A. M. Lyapunov; The general problem of the stability of motion, Int. J.\nControl, Vol. 55, No. 3, 1992, pp. 521-790. http://www.tandfonline.com/\ntoc/tcon20/55/3.\n[15] B .G. Pachpatte; Lyapunov tye integral inequalities for certain\ndifferential equations, Georgian Math. J., 4, No. 2, (1997), 139-148.\n[16] B. G. Pachpatte; Inequalities related to zeros of solutions of certain\nsecond order differential equations, Ser. Math. Inform., 16 (2001), 35-44.\n[17] B. G. Pachpatte; On Lyapunov type inequalities for certain higher order\ndifferential equations, J. Math. Anal. Appl., 195 (1995), 527-536.\n[18] Gani T. Stamov; Almost Periodic Solutions of Impulsive Differential\nEquations, Springer, (2012).\n[19] X. Yang; On Lyapunov type inequalities for certain higher order\ndifferential equations, Appl. Math. Comput., 134 (2003), 307-317.\n[20] Xiaojing Yang, Yong-In Kim, Kueiming Lo; Lyapunov-type inequality\nfor a class of even-order linear differential equations, Appl. Math.\nComput., 245 (2014), 145-151.\n[21] Xiaojing Yang, Yong-In Kim, Kueiming Lo; Lyapunov-type inequalities\nfor a class of higher-order linear differential equations, Appl. Math. Lett.,\n34 (2014) 86-89."]}