  We study the deep inelastic scattering (DIS) of a proton-targeted lepton in
the presence of gluon condensation using gauge/gravity duality. We use a
modified $AdS_5$ background where the modification parameter $c$ corresponds to
the gluon condensation in the boundary theory. Firstly, when examining the
electromagnetic field, we find that non-zero $c$ can increase the magnitude of
the field. Our goal is to find the acceptable value of $c$ for this scattering
and our method is based on setting the mass of the proton as an eigenvalue of
the baryonic state equations of the DIS to find the acceptable value of the
parameter c on the other side of the equations. Therefore in the second step,
we calculate wave function equations for the baryonic states where the mass of
the proton target requires a value contribution of $c$ as $c = 0.0120 {\rm
GeV}^4$. Proceeding by the electromagnetic field and the baryonic states, we
derive the holographic interaction action related to the amplitude of the
scattering. Finally, we compute the corresponding structure functions
numerically as functions of $x$ and $q$, which are Bjorken variables and the
lepton momentum transfers, respectively. Comparing the Jlab Hall $C$ data with
our theoretical calculations, our results are acceptable.
