Nonexistence of solutions to a fractional differential boundary value problem

We investigate new results about Lyapunov-type inequality by considering a fractional boundary value problem subject to mixed boundary conditions. We give a necessary condition for nonexistence of solutions for a class of boundary value problems involving Riemann-Liouville fractional order. The order considered here is 3 < alpha <= 4. The investigation is based on a construction of Green's function and on finding its corresponding maximum value. In order to illustrate the result, we provide an application of Lyapunov-type inequality for an eigenvalue problem and we show how the necessary condition of existence can be employed to determine intervals for the real zeros of the Mittag-Leffler function. (C) 2016 All rights reserved.