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

In this paper, we study the nonlocal fractional differential equation: \ array@l Dα₀₊u(t)+f(t,u(t))=0 , 0< t< 1,\\ u(0)=0, u(1)=η u(ξ), array . where 1 < α< 2 , 0 < ξ< 1 , ηξα-1= 1 , Dα₀₊ is the standard Riemann-Liouville derivative, f:[0,1]×[0,+∞) is continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique.