  \color{blue}{In the wake of efforts made in [EPL {\bf 97}, 41001 (2012)] and
[J. Math. Phys. {\bf 54}, 103302 (2913)], we extend them here by developing the
conventional Lagrangian treatment of a classical field theory (FT) to the
q-Klein-Gordon equation advanced in [Phys. Rev. Lett. {\bf 106}, 140601 (2011)]
and [J. Math. Phys. {\bf 54}, 103302 (2913)], and the quantum theory
corresponding to $q=\frac {3} {2}$. This makes it possible to generate a
putative conjecture regarding black matter. Our theory reduces to the usual FT
for $q\rightarrow 1$.}
