Abstract
Using a perturbation argument, we establish the existence and uniqueness of a positive continuous solution for the following superlinear RiemannLiouville fractional boundary-value problem
D-alpha u(x) - u(x)phi(x, u (x)) = 0, 0 < x < 1,
u(0) = u'(0) = lim (x -> 0+) x(4-alpha) u"(x) = 0, u" (1) = a > 0;
where 3 < alpha <= 4 and phi(x, t) satisfies a suitable integrability condition.