We discuss boundary value problems for Riemannâ€“Liouville fractional differential equations with certain fractional integral boundary conditions. Such boundary conditions are different from the widelyâ€¦ (More)

In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation xâ€²â€²â€² + q(t)x = 0 . Our work provides the sharpest results in the literature and makesâ€¦ (More)

In this article, we obtain Lyapunov-type inequalities for certain odd order linear boundary-value problems. Our inequalities involve integrals of both q+(t) and qâˆ’(t) in addition to that of |q(t)|.â€¦ (More)

The Lyapunov inequality for second order linear differential equations has been extended to higher order linear differential equations in various forms. It has also been extended to second and thirdâ€¦ (More)

A model describing the mobility tensor for electrons in strained Si layers as a function of strain is presented. It includes the effect of strain-induced splitting of the conduction band valleys inâ€¦ (More)

We study linear fractional boundary value problems consisting of an Î±-th order Riemann-Liouville fractional differential equation with 2 < Î± â‰¤ 3 and certain fractional boundary conditions. We deriveâ€¦ (More)