Lyapunov-type inequalities for a nonlinear fractional boundary value problem

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 <= 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.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 <= 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.A