Abstract
In this work, we deal with the existence of extremal quasisolutions for the following finite system of nonlinear fractional differential equation (C)D(q)u (t) + f (t, u (t)) = 0 in (0, 1), u(0) - alpha u' (0) = lambda, u(1) + beta u'(1) = mu,where 1 < q < 2,alpha,beta is an element of (R+)(n) , lambda, mu epsilon R-n and f is an element of C([0, 1] x R-n ,R-n) and D-C(q) is the Caputo fractional derivative of order q. We shall prove constructive existence results for a class of nonlinear equations by the use of iterative method technique combined with upper and lower quasisolutions. We construct a pair of sequences of coupled lower and upper quasisolutions which converge uniformly to extremal quasisolutions. Then, a uniqueness result is given under additional conditions on the nonlinearity f.