@Article{Agarwal1969, author=" R. P. Agarwal", title=" Certain fractional q-integrals and q-derivatives", journal="Proc. Cambridge Philos. Soc.", year="1969", pages="365-370. ", volume="66" } @Article{Aktas2013, author="M. F. Aktas", title="Lyapunov-type inequalities for a certain class of n-dimensional quasilinear systems", journal=" Electron. J. Differ. Equat.", year="2013", pages="1-8. ", volume="67" } @Article{Al-Salam1966/1967, author=" W. A. Al-Salam", title="Some fractional q-integrals and q-derivatives", journal="Proc. Edinb. Math. Soc.", year="1966/1967", pages="135-140. ", volume="15" } @Article{Atici2007, author="F. M. Atici, P. W. Eloe", title="Fractional q-calculus on a time scale", journal="J. Nonlinear Math. Phys.", year="2007", pages=" 333-344. ", volume="14" } @Article{Çakmak2010, author=" D. Çakmak", title="Lyapunov-type integral inequalities for certain higher order differential equations", journal="Appl. Math. Comput.", year="2010", pages=" 368-373. ", volume="216" } @Article{akmak2013, author="D. Ç akmak", title="On Lyapunov-type inequality for a class of nonlinear systems", journal="Math. Inequal. Appl.", year="2013", pages="101-108. ", volume="16" } @Article{Cheng1983, author="S. S. Cheng", title="A discrete analogue of the inequality of Lyapunov", journal="Hokkaido Math. J.", year="1983", pages="105-112. ", volume="12" } @Article{Eliason1970, author="S. B. Eliason", title="A Lyapunov inequality for a certain nonlinear differential equation", journal="J. London Math. Soc.", year="1970", pages="461-466. ", volume="2" } @Article{El-Shahed2010, author="M. El-Shahed, H. A. Hassan", title="Positive solutions of q-difference equation", journal="Proc. Amer. Math. Soc.", year="2010", pages="1733-1738.", volume="138" } @Book{Ernst 2000, author="T. Ernst ", title="The History of q-Calculus and a New Method", year="2000", publisher="Department of Mathematics", address=" Uppsala University" } @Article{Ferreira2010, author=" R. A. C. Ferreira", title="Nontrivial solutions for fractional q-difference boundary value problems", journal="Electron. J. Qual. Theory Differ. Equ.", year="2010", pages=" 1-10. ", volume="70" } @Article{Ferreira2011, author="R. A. C. Ferreira", title="Positive solutions for a class of boundary value problems with fractional q-differences ", journal="Comput. Math. Appl.", year="2011", pages=" 367-373. ", volume="61" } @Article{Ferreira2013, author="R. A. C. Ferreira", title=" A Lyapunov-type inequality for a fractional boundary value problem", journal="Fract. Calc. Appl. Anal.", year="2013", pages="978-984. ", volume="16" } @Article{Hartman1951, author="P. Hartman, A. Wintner", title="On an oscillation criterion of Liapounoff", journal="Amer. J. Math.", year="1951", pages="885-890. ", volume="73" } @Article{He2012, author=" X. He, X. H. Tang", title="Lyapunov-type inequalities for even order differential equations", journal="Commun. Pure Appl. Anal.", year="2012", pages=" 465-473.", volume="11" } @Article{Jackson1909, author="F. H. Jackson", title="On q-functions and a certain difference operator", journal="Trans. Roy Soc. Edin.", year="1909", pages="253-281. ", volume="46" } @Article{Jackson1910, author=" F. H. Jackson", title=" On q-definite integrals", journal="Quart. J. Pure and Appl. Math.", year="1910", pages="193-203. ", volume="41" } @Book{Kac2002, author="V. Kac, P. Cheung", title="Quantum Calculus", year="2002", publisher="Springer", address=" New York" } @Book{Kilbas2006, author=" A. A. Kilbas, H. M. Srivastava, J. J. Trujillo", title=" Theory and Applications of Fractional Differential Equations", year="2006", publisher="North-Holland Mathematics Studies 204, Elsevier", address="Amsterdam" } @Article{Kwong1981, author="M. K. Kwong", title="On Lyapunov's inequality for disfocality", journal="J. Math. Anal. Appl.", year="1981", pages="486-494. ", volume="83" } @Article{Liang2012, author=" S. Liang, J. Zhang ", title="Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences", journal=" J. Appl. Math. Comput.", year="2012", pages=" 277-288.", volume="40" } @Book{Lyapunov1949, author="A. M. Lyapunov", title="Problème général de la stabilité du mouvement", year="1949", publisher="Ann. Math. Stud. vol. 17, Princeton Univ. Ptess", address="Princeton" } @Article{Ma2011, author=" J. Ma, J. Yang", title="Existence of solutions for multi-point boundary value problem of fractional q-difference equation", journal="Electron. J. Qual. Theory Differ. Equ.", year="2011", pages="10 pages. ", volume="2011" } @Article{Pachpatte1995, author="B. G. Pachpatte", title="On Lyapunov-type inequalities for certain higher order differential equations", journal="J. Math. Anal. Appl.", year="1995", pages=" 527-536. ", volume="195" } @Article{Pachpatte1997, author="B. G. Pachpatte", title="Lyapunov type integral inequalities for certain differential equations", journal="Georgian Math. J.", year="1997", pages="139-148. ", volume="4" } @Article{Parhi1999, author="N. Parhi, S. Panigrahi ", title="On Liapunov-type inequality for third-order differential equations ", journal="J. Math. Anal. Appl.", year="1999", pages="445-460. ", volume="233" } @Article{Rajković2007, author="P. M. Rajković, S. D. Marinković, M. S. Stanković ", title="On q-analogues of caputo derivative and Mittag-Leffler function", journal="Fract. Calc. Appl. Anal.", year="2007", pages="359-373. ", volume="10" } @Article{Tariboon2014, author="J. Tariboon, S. K. Ntouyas", title="Quantum integral inequalities on finite intervals", journal="J. Inequal. Appl.", year="2014", pages="13 pages. ", volume="2014" } @Article{Tariboon2015, author="J. Tariboon, S. K. Ntouyas, P. Agarwal", title="New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations", journal="Adv. Difference Equ.", year="2015", pages="19 pages. ", volume="2015" } @Article{Yang2003, author="X. Yang", title="On Liapunov-type inequality for certain higher-order differential equations", journal="Appl. Math. Comput.", year="2003", pages="307-317.", volume="134" }