POSITIVE SOLUTIONS FOR SYSTEMS OF COMPETITIVE FRACTIONAL DIFFERENTIAL EQUATIONS

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.