Eventual differentiability of functional differential equations in Banach spaces

This paper concerns the regularity of a functional differential equation in the form: , t>0, where A is the generator of an analytic semigroup on a Banach space X, and B1,B2 are α(γ−A)-bounded linear operator for 0<α<1. By spectral analysis, it is shown that the associated solution semigroup of this equation is eventually differentiable.