Periodic solutions of fractional degenerate differential equations with delay in Banach spaces

We characterize the L-p-well-posedness (resp. B-p, q(s)-well-posedness) for the fractional degenerate differential equations with finite delay: D-alpha(Mu)(t) = Au(t) + Gu(t)' + Fu(t) + f(t), (t is an element of [0, 2 pi]), where alpha > 0 is fixed and A, M are closed linear operators in a Banach space X satisfying D(A) boolean AND D(M) not equal {0}, F and G are bounded linear operators from L-p([-2 pi, 0]; X) (resp. B(p, q)s([-2 pi, 0]; X)) into X. We also give a new example to which our abstract results may be applied.