  In this paper, we study regularity of solutions to linear evolution equations
of the form $dX+AXdt=F(t)dt$ in a Banach space $H$, where $A$ is a sectorial
operator in $H$ and $A^{-\alpha} F \, (\alpha>0)$ belongs to a weighted
H\"{o}lder continuous function space. Similar results are obtained for linear
evolution equations with additive noise of the form $dX+AXdt=F(t)dt+G(t)dW(t)$
in a separable Hilbert space $H$, where $W(t)$ is a cylindrical Wiener process.
Our results are applied to a model arising in neurophysiology, which has been
proposed by Walsh \cite{Walsh}.
