  We investigate analytically as well as numerically effects of nonlinear
Born-Infeld (BI) electrodynamics on the properties of (1+1)-dimensional
holographic $p$-wave superconductor in the context of gauge/gravity duality. We
consider the case in which the gauge and vector fields backreact on the
background geometry. We apply the Sturm-Liouville eigenvalue problem for the
analytical approach as well as the shooting method for the numerical
calculations. In both methods, we find out the relation between critical
temperature $T_{c}$ and chemical potential $\mu$ and show that both approaches
are in good agreement with each other. We find that if one strengthen the
effect of backreaction as well as nonlinearity, the critical temperature
decreases which means that the condensation is harder to form. We also explore
the conductivity of the one-dimensional holographic $p$-wave superconductor for
different values of b and $T/T_{c}$. We find out that the real and imaginary
parts of the conductivity have different behaviors in higher dimensions. The
effects of different values of temperature is more apparent for larger values
of nonlinearity parameter. In addition, for the fixed value of $T/T_{c}$ by
increasing the effect of nonlinearity we observe larger values for Drude-like
peak in real part of conductivity and deeper minimum for imaginary part.
