Abstract
Using potential theory arguments, we study the existence and boundary behavior of positive solutions in the space of weighted continuous functions, for the fractional differential system
D(alpha)u(x) + p(x)u(a1)(x)v(b1)(x) = 0 in (0, 1), lim(x -> 0+) x(1-alpha)u(x) = lambda >0,
D(beta)v(x) + q(x)v(a2)(x)u(b2)(x) = 0 in (0, 1), lim(x -> 0+)x(1-beta)v(x) = mu >0,
where alpha, beta is an element of(0, 1), a(i) > 1, b(i) > 0 for i is an element of {1, 2} and p,q are positive continuous functions on (0, 1) satisfying a suitable condition relying on fractional potential properties.