In this talk, we combine tools from classical fractional calculus and the Rough Path Theory to study the existence and uniqueness of mild solutions to evolutions equations driven by a Hölder continuous function with Hölder exponent in the interval $(1/3,1/2)$. The stochastic integral is given by a generalization of the well-known Young integral and can be defined independently of the initial condition. In order to formulate an operator equation solving the problem we need a second equation for the so called area in the space of tensors, and the key ingredient to get this is to construct a tensor depending on the noise path and also on the semigroup. We prove in a first step the existence of a unique Hölder continuous solution of the system of equations, consisting of the path and the area components, if the nonlinear term and the initial condition are sufficiently smooth. In a second part, we also prove similar results when considering more general initial states, by modifying accordingly the phase space. The abstract theory is applicable to evolution equations driven by a fractional Brownian motion $B^H$ with Hurst parameter $H in (1/3,1/2]$. One important result is that the pathwise definition of the stochastic integral allows to prove that the solution process generates a random dynamical system. This is a join work with Kening Lu (BYU, Provo) and Björn Schmalfuss (Universität Jena).