On the well-posedness of degenerate fractional differential equations in vector valued function spaces

We characterize completely the well-posedness on the vector-valued Hölder and Lebesgue spaces of the degenerate fractional differential equation D ^α (Mu)(t) = Au(t) + f(t), t ∈ ? by using vector-valued multiplier results in the spaces C ^γ (?;X) and L ^p (?;X), where A and M are closed linear operators defined on the Banach space X, 0 < γ < 1, 1 < p < ∞, the fractional derivative is understood in the sense of Caputo and α is positive.