  The Wiener's path integral plays a central role in the studies of Brownian
motion. Here we derive exact path-integral representations for the more general
\emph{fractional} Brownian motion (fBm) and for its time derivative process --
the fractional Gaussian noise (fGn). These paradigmatic non-Markovian
stochastic processes, introduced by Kolmogorov, Mandelbrot and van Ness, found
numerous applications across the disciplines, ranging from anomalous diffusion
in cellular environments to mathematical finance. Still, their exact
path-integral representations were previously unknown. Our formalism exploits
the Gaussianity of the fBm and fGn, relies on theory of singular integral
equations and overcomes some technical difficulties by representing the action
functional for the fBm in terms of the fGn for the sub-diffusive fBm, and in
terms of the derivative of the fGn for the super-diffusive fBm. We also extend
the formalism to include external forcing. The exact and explicit path-integral
representations open new inroads into the studies of the fBm and fGn.
