Existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations

In this article, by using the fixed point theorem, existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations D 0 + α u ( t ) + λ a ( t ) f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = 0 is considered, where 1 < α < 2 is a real number, D 0 + α is the standard Riemann-Liouville derivate, λ is a positive parameter and a ( t ) ∈ C ([0, 1], [0, ∞)), f ( t , u ) ∈ C ([0, 1] × [0, ∞), [0, ∞)). MSC(2010): 34B18.