Fractional Lyapunov inequalities on spherical shells

Some Discrete Fractional Lyapunov–type Inequalities

In this work we obtain Lyapunov-type inequalities for two-point conjugate and rightfocal boundary value problems depending on discrete fractional operators Δα , 1 < α 2 .

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

‎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, ‎...

Two generalized Lyapunov-type inequalities for a fractional p-Laplacian equation with fractional boundary conditions

In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.

Controllable vortex chirality switching on spherical shells

Nematic textures in spherical shells.

The equilibrium texture of nematic shells is studied as a function of their thickness. For ultrathin shells the ground state has four short 1/2 disclination lines but, as the thickness of the film increases, a three-dimensional escaped configuration composed of two pairs of half-hedgehogs becomes energetically favorable. We derive an exact solution for the nematic ground state in the one Frank ...