($\sigma(\cdot)=0$ in Eq. (\[spde-uniq\])) were studied in Maslowski and Nualart [@maslowski2003evolution] and Garrido-Atienza, Lu, and Schmalfuss [@Garrido-Atienzalu2010], and recently by Chen, Gao, Garrido-Atienza, and Schmalfuss [@chen2014pathwise] when the stochastic evolution equations are driven by a Hölder continuous function with Hölder exponent in $(\frac{1}{2},1)$ and with nontrivial multiplicative noise. Guerra and Nualart [@Guerra2008] proved an existence and uniqueness theorem of solutions to multidimensional SDEs driven by fBm with Hurst parameter $H>\frac{1}{2}$ and Bm. Using the theory of Wiener integral, Caraballo, Garrido-Atienza and Taniguchi [@caraballo2011existence] investigated the existence and exponential behavior of solutions to stochastic delay evolution equations with an additive fractional noise.

However, the method proposed in [@Guerra2008] fails for the infinite-dimensional case and the method in [@caraballo2011existence] fails for the multiplicative fractional noise case. The main difference (and, of course, difficulty) is that we cannot apply directly the existence and uniqueness results in [@Garrido-Atienzalu2010; @Guerra2008] and [@caraballo2011existence; @chen2014pathwise]. Thus, to close this gap, as one of two main results of our paper, we obtain pathwise unique solutions to Eq. (\[spde-uniq\]) relying on a pathwise approach, a stopping time technique and an approximation for the fractional noise (See Theorem \[mixuniq\]).

Then, as the second main result, this paper will establish an 