Positive solutions for some RiemannLiouville fractional boundary value problems

We study the existence and global asymptotic behavior of positive continuous solutions to the following nonlinear fractional boundary value problem (Pλ){ D^αu (t) = λf (t, u(t)), t ∈ (0, 1) lim t^2−α u(t) = µ, u(1) = ν, t→0+ where 1 α ≤ 2, Dα is the Riemann-Liouville fractional derivative, and λ, µ and ν are nonnegative constants such that µ + ν 0. Our purpose is to give two existence results for the above problem, where f (t, s) is a nonnegative continuous function on (0, 1) × [0, ∞), nondecreasing with respect to the second variable and satisfying some appropriate integrability condition. Some examples are given to illustrate our existence results.