Existence and multiplicity of positive solutions for boundary-value problems of non-linear fractional differential equations

Abstract

The positive solutions under particular boundary circumstances arising from non-linear fractional differential equations were recently constructed [S. Zhang, Positive. Solutions for boundary-value problems of nonlinear fractional differential equations. Electron. J. Differ. Eq., Vol. 2006, 36, 1-12, 2006]. In this paper, we also discuss the existence and multiplicity of positive solutions for the following nonlinear fractional differential equation boundaryvalue problem (Equation Presented) where 2 < ? ? 3 is a real number, and D?0+ is the Caputo's fractional derivative, and f: [0,1] × [0,+?) ? [0,+?) is continuous. By using Krasnoesel'skii's fixed-point theorem on cones, we obtain various results on the existence of positive solutions of the boundary-value problem.