An eigenvalue problem for a fractional differential equation with an iterated fractional derivative

Abstract

This paper concerns the investigation of an eigenvalue problem for a nonlinear fractional differential equation. Using the properties of the Green function, Banach contraction principle, Leray-Schauder nonlinear alternative and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation are considered. Some sufficient conditions for the existence of at least one positive solution is established. Some examples are presented to illustrate the main results.