New classes of Lyapunov type inequalities of fractional $Delta$-difference Sturm-Liouville problems with applications

Abstract

‎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.