Lyapunov inequality for a boundary value problem involving conformable derivative

Abstract

We consider a boundary value problem involving conformable derivative of order $\alpha ,$ $1<\alpha <2$ and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's fixed-point theorem. \ Futhermore, we give the Lyapunov inequality for the corresponding problem.

This is a preprint of a paper Accepted 15 May 2017 and whose final and definite form is published in Prog. Frac. Diff. Appl. See http://dx.doi.org/10.18576/pfda

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• Lyapunov-type inequality for a fractional boundary value problem with natural conditions