  Taking into consideration of Kaniadakis entropy associated with the apparent
horizon of Friedmann-Robertson-Walker (FRW) Universe and using the
gravity-thermodynamics conjecture, a new cosmological scenarios emerges based
on corrected Friedmann equations, which contains a correction term $
\alpha\left(H^2+\frac{k}{a^2}\right)^{-1}$ where $\alpha\equiv\frac{K^2
\pi^2}{2 G^2}$ and $K$ is Kaniadakis parameter. We show that it is possible to
reconstruct the parameters of the model, in terms of cosmographic parameters$\{
q, j, s\}$ analytically. For the flat universe, the parameters can be
reconstructed in terms of only two cosmographic parameters $\{q, j\}$. The
advantage of this analytical reconstruction is that it provides the possibility
to test observational measurements on Kaniadakis cosmology using directly
measurable cosmographic parameters.
  As an interesting result is that without any assumption about the value of
$\Lambda$, we found that the set $\{q_{0}=-0.708, j_{0}=1.137\}$ automatically
gives $\Lambda\simeq0$ and $\{\Omega_{m0}\simeq0.325,\Omega_{\alpha0}=0.671\}$.
This result is in excellent agrement with pervious observational studies.
Reconstructing the evolution of deceleration parameter against redshift $z$ for
these values, shows that the correction term could plays the role of dark
energy without any dark energy component or cosmological constant $\Lambda$.
Finally, we formulate the deviation parameter in terms of $\{q,j\}$ which
reflects the deviation of the model from $\Lambda CDM$ model. We Show that the
deviation factor is very sensitive to the jerk parameter $j$, while the
$\Omega_{m0}$ is sensitive to deceleration parameter $q_{0}$. Hence, the set
$\{j,q\}$ can be regarded as useful parameters to test the theoretical and
observational studies in Kaniadakis cosmology.
