Nonexistence of solutions to a fractional differential boundary value problem

Abstract

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 < α ≤ 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.

Recent Developments of Lyapunov–Type Inequalities for Fractional Differential Equations

“…where q : [a, b] → R is a continuous function. The Lyapunov-type inequality derived for problem (26)…”

“…In 2016, Al-Qurashi and Ragoub [26] obtained a Lyapunov-type inequality for a fractional boundary value problem:…”