%0 Journal Article %T New classes of Lyapunov type inequalities of fractional $\Delta$-difference Sturm-Liouville problems with applications %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Ghanbari, K. %A Gholami, Y. %D 2017 %\ 04/01/2017 %V 43 %N 2 %P 385-408 %! New classes of Lyapunov type inequalities of fractional $\Delta$-difference Sturm-Liouville problems with applications %K Discrete fractional calculus‎ %K ‎discrete fractional Sturm-Liouville problem‎ %K ‎Lyapunov type inequalities‎ %K ‎stability‎ %K ‎Mittag-Leffler type functions‎ %R %X ‎In this paper‎, ‎we consider a new study about fractional $\Delta$-difference equations‎. ‎We consider two special classes of Sturm-Liouville problems equipped with fractional $\Delta$-difference operators‎. ‎In couple of steps‎, ‎the Lyapunov type inequalities for both classes will be obtained‎. ‎As application‎, ‎some qualitative behaviour of mentioned fractional problems such as stability‎, ‎spectral‎, ‎disconjugacy and some interesting results about zeros of (oscillatory) solutions will be concluded. %U http://bims.iranjournals.ir/article_938_599bea256ce7e3704a0d85dc06ff4b99.pdf