  In this work, we obtain a Lyapunov-type and a Hartman-Wintner-type
inequalities for a linear and a nonlinear fractional differential equation with
generalized Hilfer operator subject to Dirichlet-type boundary conditions. We
prove existence of positive solutions to a nonlinear fractional boundary value
problem. As an application, we obtain a lower bound for the eigenvalues of
corresponding equations.
