Existence of positive solutions to a coupled system of fractional differential equations

We consider the following system of fractional differential equations D0 alpha+x(t) + f(t,x(t),y(t)) = 0, t is an element of(0,1),n-1 < alpha <= n, D-0(beta)+ y(t) + g(t,x(t),y(t)) = 0, t is an element of(0,1),n-1 < beta <= n, x((i))(0) = y((i))(0) = 0, i = 0,1,2,...,n-2, [D(0+)(gamma)x(t)](t=1) = 0, 2 <= gamma <= n-2, [D-0+(delta) y(t)](t=1) = 0, 2 <= delta <= n-2, where n 3, D-0+(alpha) is the Riemann-Liouville fractional derivative of order ,f,g : [0,1]x[0,)x[0,)[0,). Sufficient conditions are provided for the existence of positive solutions to the considered problem. Copyright (c) 2014 John Wiley & Sons, Ltd.