Positive solutions for a class of fractional 3-point boundary value problems at resonance

Abstract

In this paper, we study the nonlocal fractional differential equation: {D0+αu(t)+f(t,u(t))=0,0 < α< 2 , 0 < ξ< 1 , ηξα−1= 1 , D0+α is the standard Riemann-Liouville derivative, f: [0 , 1] × [0 , + ∞) → R is continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique.