  This paper addresses the exponential stability of the trivial solution of
some types of evolution equations driven by H\"older continuous functions with
H\"older index greater than $1/2$. The results can be applied to the case of
equations whose noisy inputs are given by a fractional Brownian motion $B^H$
with covariance operator $Q$, provided that $H\in (1/2,1)$ and ${\rm tr}(Q)$ is
sufficiently small.
