Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations

Some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worth mentioning that when alpha = 1 the initial value problem D-alpha[y(t)e(beta t)] = f(t,y(t))e(beta t), t is an element of [t(0),infinity), t(0) >= 0, 0 < alpha < 1, y(t) = phi(t), t(0) - h <= t <= t(0), reduces to a classical dissipative differential equation with delays as in Caraballo et al.'s work ( 2005).