TY - JOUR ID - 938 TI - New classes of Lyapunov type inequalities of fractional $\Delta$-difference Sturm-Liouville problems with applications JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Ghanbari, K. AU - Gholami, Y. AD - Department of Applied Mathematics‎, ‎Sahand University of‎ ‎Technology‎, ‎P.O‎. ‎Box 51335-1996‎, ‎Tabriz‎, ‎Iran. Y1 - 2017 PY - 2017 VL - 43 IS - 2 SP - 385 EP - 408 KW - Discrete fractional calculus‎ KW - ‎discrete fractional Sturm-Liouville problem‎ KW - ‎Lyapunov type inequalities‎ KW - ‎stability‎ KW - ‎Mittag-Leffler type functions‎ DO - N2 - ‎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. UR - http://bims.iranjournals.ir/article_938.html L1 - http://bims.iranjournals.ir/article_938_599bea256ce7e3704a0d85dc06ff4b99.pdf ER -