Some results for two classes of two-point local fractional proportional boundary value problems

Abstract

In this paper, we consider two classes of boundary value problems in theframe of local proportional fractional derivatives. For both of theseclasses, we obtain the associated Green's functions and discuss theirproperties. Using these properties, we go about the uniqueness of thesolutions. In addition, we establish Lyapunov and Hartman-Wintner typeinequalities and build sharp estimated for the unique solutions of theconsidered equations.