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| We show the existence of a smallest eigenvalue for the fractional linear differential equation $D_{0+}^{\alpha} u+\lambda p(t)u=0$, $0< t< 1$, satisfying the boundary conditions $u(0)=u(1)=0$. This is accomplished by showing the operator $Mu(t)=\int^1_0 G(t,s)p(s)u(s)ds$, where $G(t,s)$ is the appropriate Green's function, is a $u_0$-positive operator. Some consequences of this existence will be explored. |
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