  We study the problem of stabilization for a class of evolution systems with
fractional-damping. After writing the equations as an augmented system we prove
in this article first that the problem is well posed. Second, using the
LaSalle's invariance principle we show that the energy of the system is
Strongly stable. Then, based on a resolvent approach we show a luck of uniform
stabilization. Next, using multiplier techniques combined with the frequency
domain method, we shall give a polynomially stabilization result under some
consideration on the stabilization of an auxiliary dissipating system. Finally,
we give some applications to the wave equation.
