Positive solutions to singular Dirichlet-type boundary value problems of nonlinear fractional differential equations

Abstract

In this paper, by using the properties of the Green function, $u_{0}$ -positive operator and Gelfand’s formula, some properties of the first eigenvalue corresponding to the relevant operator are obtained. Based on these properties, the fixed point index of the nonlinear operator is calculated explicitly and some sufficient conditions for the existence and uniqueness results of positive solution are established.