  We provide an analytical as well as a numerical study of the holographic
$s$-wave superconductors in Gauss-Bonnet gravity with Power-Maxwell
electrodynamics. We limit our study to the case where scalar and gauge fields
do not have an effect on the background metric. We use a variational method,
based on Sturm-Liouville eigenvalue problem for our analytical study, as well
as a numerical shooting method in order to compare with our analytical results.
Interestingly enough, we observe that unlike Born-Infeld-like nonlinear
electrodynamics which decrease the critical temperature compared to the linear
Maxwell field, the Power-Maxwell electrodynamics is able to increase the
critical temperature of the holographic superconductors in the sublinear
regime. We find that requiring the finite value for the gauge field on the
asymptotic boundary $r\rightarrow \infty$, restricts the power parameter, $q$,
of the Power-Maxwell field to be in the range $1/2<q<{(d-1)}/{2}$. Our study
indicates that it is quite possible to make condensation \emph{easier} as $q$
\emph{decreases} in its allowed range. We also find that for all values of $q$,
the condensation can be affected by the Gauss-Bonnet coefficient $\alpha$.
However, the presence of the Gauss-Bonnet term makes the transition slightly
harder. Finally, we obtain an analytic expression for the order parameter and
thus obtain the associated critical exponent near the phase transition. We find
that the critical exponent has its universal value of $\beta=1/2$ regardless of
the parameters $q$, $\alpha$ as well as dimension $d$, consistent with
mean-field values obtained in previous studies.
