Lyapunov-type inequalities for a nonlinear fractional boundary value problem

Abstract

In this paper, we obtain a Lyapunov-type and a Hartman–Wintner-type inequalities for a nonlinear fractional hybrid equation with left Riemann–Liouville and right Caputo fractional derivatives of order $$1/2<\alpha \le 1,$$ subject to Dirichlet boundary conditions. It is also shown that failure of the Lyapunov-type and Hartman–Wintner-type inequalities, corresponding nonlinear boundary value problem has only trivial solutions. In the case $$\alpha =1$$ , our results coincide with the classical Lyapunov and Hartman–Wintner inequalities, respectively.