Electronic Journal of Differential Equations (Sep 2017)
Lyapunov-type inequalities for $\alpha$-th order fractional differential equations with 2<$\alpha\le3$ and fractional boundary conditions
Abstract
We study linear fractional boundary value problems consisting of an $\alpha$-th order Riemann-Liouville fractional differential equation with 2<$\alpha\leq 3$ and certain fractional boundary conditions. We derive several Lyapunov-type inequalities and apply them to establish nonexistence, uniqueness, and existence-uniqueness of solutions for related homogeneous and nonhomogeneous linear fractional boundary value problems. As a special case, our work extends some existing results for third-order linear boundary value problems.
