\(C^{\alpha}\)-Hölder classical solutions for non-autonomous neutral differential equations (Q628766)

The authors study the existence of \(C^{\alpha}\)-Hölder classical solutions for the following neutral differential equation \[ d/(dt)[x(t)+g(t,x_{t})] = A(t)x(t)+f(t,x_{t}), ~t\in [0,a], ~x_0 = \Phi \in C:=C([-r,0],X), \] where \(X\) is a Banach space, \(A(t)_{t\in [0,a]}\) is a family of sectorial operators defined on a common domain \(D\), and \(f,g:[0,a]\times C\rightarrow X\) are appropriate functions.