Commenced in January 2007
Paper Count: 31100
Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems
Abstract: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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1124641Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1231
 T. Abdeljawad; On conformable fractional calculus, J. Comput. Appl. Math., 279, (2015), 57-66.
 Mustafa Fahri Aktas¸; On the multivariate Lyapunov inequalities, Appl. Math. Comput. 232 (2014) 784-786.
 Mustafa Fahri Aktas¸, Devrim C¸ akmak, Aydin Tiryaki; On Lyapunov type inequalities of a three-point boundary value problem for third order linear differential equations, Appl. Math. Lett., (2015), In Press.
 Drumi Bainov, Valery Covachev; Impulsive Differential Equations With a Small Parameter, World Scientific, (1994).
 Sougata Dhar, Qingkai Kong; Liapunov-type inequalities for third-order half-linear equations and applications to boundary value problems, Nonlinear Anal. Theory, Methods and Applications, 110 (2014), 170-181.
 Rui A.C. Ferreira; A Lyapunov-type inequality for a fractional boundary value problem, Fract. Calc. Appl. Anal., Vol. 16, No 4 (2013), pp. 978-984; DOI: 10.2478/s13540-013-0060-5.
 Rui A. C. Ferreira; On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function, J. Math. Anal. Appl., 412, 2 (2014), 1058-1063.
 G. Sh. Guseinov, B. Kaymakc¸alan; Lyapunov inequalities for discrete linear Hamiltonian systems, Comput. Math. Appl., 45, (2003), 1399-1416.
 G. Sh. Guseinov, A. Zafer; Stability criterion for second order linear impulsive differential equations with periodic coefficients, Math. Nachr., 281, No. 9, (2008), 1273-1282.
 G. Sh. Guseinov, A. Zafer; Stability criteria for linear periodic impulsive Hamiltonian systems, J. Math. Anal. Appl., 335, (2007), pp. 1195-1206.
 Mohamad Jleli, Bessem Samet; Lyapunov type inequalities for a fractional differential equation with mixed boundary conditions, Math. Inequal. Appl., Vol. 18, No. 2 (2015), 443-451.
 R. Khalil, M. Al Horani, A. Yousef, M. Sababheh; A new definition of fractional derivative, J. Comput. Appl. Math., 264, (2014), 65-70.
 Xin-Ge Liu, Mei-Lan Tang; Lyapunov-type inequality for higher order difference equations, Appl. Math. Comput. 232 (2014) 666-669.
 A. M. Lyapunov; The general problem of the stability of motion, Int. J. Control, Vol. 55, No. 3, 1992, pp. 521-790. http://www.tandfonline.com/ toc/tcon20/55/3.
 B .G. Pachpatte; Lyapunov tye integral inequalities for certain differential equations, Georgian Math. J., 4, No. 2, (1997), 139-148.
 B. G. Pachpatte; Inequalities related to zeros of solutions of certain second order differential equations, Ser. Math. Inform., 16 (2001), 35-44.
 B. G. Pachpatte; On Lyapunov type inequalities for certain higher order differential equations, J. Math. Anal. Appl., 195 (1995), 527-536.
 Gani T. Stamov; Almost Periodic Solutions of Impulsive Differential Equations, Springer, (2012).
 X. Yang; On Lyapunov type inequalities for certain higher order differential equations, Appl. Math. Comput., 134 (2003), 307-317.
 Xiaojing Yang, Yong-In Kim, Kueiming Lo; Lyapunov-type inequality for a class of even-order linear differential equations, Appl. Math. Comput., 245 (2014), 145-151.
 Xiaojing Yang, Yong-In Kim, Kueiming Lo; Lyapunov-type inequalities for a class of higher-order linear differential equations, Appl. Math. Lett., 34 (2014) 86-89.