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In this work, we obtain a Lyapunov-type and a Hartman-Wintner-typeinequalities for a linear and a nonlinear fractional differential equation withgeneralized Hilfer operator subject to Dirichlet-type boundary conditions. Weprove existence of positive solutions to a nonlinear fractional boundary valueproblem. As an application, we obtain a lower bound for the eigenvalues ofcorresponding equations.

Lyapunov and Hartman-Wintner type inequalities for a nonlinear fractional boundary value problem with generalized Hilfer derivative