  We investigate the holographic $p$-wave superconductors in the presence of
the higher order corrections on the gravity as well as on the gauge field side.
On the gravity side, we add the Gauss-Bonnet curvature correction terms, while
on the gauge field side we take the nonlinear Lagrangian in the form $F + b
F^2$, where F is the Maxwell Lagrangian and b indicates the strength of
nonlinearity. We employ the shooting method for the numerical calculations in
order to obtain the ratio of the critical temperature $T_c$ over $\rho^
{1/(d-2)}$. We observe that by increasing the values of the mass and the
nonlinear parameters the critical temperature decreases and thus the
condensation becomes harder to form. In addition, the stronger Gauss-Bonnet
parameter $\alpha$ hinders the superconducting phase in Gauss-Bonnet gravity.
Furthermore, we calculate the electrical conductivity based on the holographic
setup. The real and imaginary parts are related to each other by Kramers-Kronig
relation which indicates a delta function and pole in low frequency regime,
respectively. However, at enough large frequencies the trend of real part can
be interpreted by $Re[\sigma] = \omega^{(d-4)}$. Moreover, in holographic model
the ratio $\omega_g/T_c$ is always much larger than the BCS value $3.5$ due to
the strong coupling of holographic superconductors. In both gravity kinds,
decreasing the temperature or increasing the effect of nonlinearity shifts the
gap frequency toward larger values. Besides, the gap frequency is occurred at
larger values by enlarging the Gauss-Bonnet parameter. In general, the behavior
of conductivity depends on the choice of the mass, the nonlinear and the
Gauss-Bonnet parameters.
