Smallest Eigenvalues for a Right Focal Boundary Value Problem

Abstract

Abstract We establish the existence of smallest eigenvalues for the fractional linear boundary value problems D 0 + α u + λ 1 p ( t ) u = 0 $D_{0 + }^\alpha u + {\lambda _1}p\left( t \right)u = 0$ and D 0 + α u + λ 2 q ( t ) u = 0 $D_{0 + }^\alpha u + {\lambda _2}q\left( t \right)u = 0$ , 0<t<1 with each satisfying the right focal boundary conditions u ( 0 ) = u ′ ( 1 ) = 0 $u\left( 0 \right) = u'\left( 1 \right) = 0$ . A comparison result is then obtained.