Abstract
Using the Schauder fixed point theorem, we prove an existence of positive solutions for the fractional differential problem in the half line R+ = (0, infinity):
D(alpha)u = f(x, u), lim(x -> 0+) u(x) = 0,
where alpha is an element of (1; 2] and f is a Borel measurable function in R+ x R+ satisfying some appropriate conditions.