Abstract
We consider the semilinear fractional boundary value problem
D-beta(1/b(x)D(alpha)u) = a(x)u(sigma) in (0, infinity)
with the conditions lim(x ->)(0)x(2)(-beta) 1/b(x) D(alpha)u(x) = lim(x ->infinity) x(1)(-beta) 1/b(x)D(alpha)u(x) = 0 and lim(x -> 0) x(2)(-alpha)u(x) = 0, where beta, alpha is an element of (1, 2), sigma is an element of (-1, 1) and D-beta, D-alpha stand for the standard Riemann-Liouville fractional derivatives. The functions a, b : (0, infinity) -> R are nonnegative continuous functions satisfying some appropriate conditions. The existence and the uniqueness of a positive solution are established. Also, a description of the global behavior of this solution is given.