  In this contribution we consider sequences of monic polynomials orthogonal
with respect to a Sobolev-type inner product \[ \langle f,g \rangle _{S}:=
\langle {\bf u}, f g\rangle +N (\mathscr D_q f)(\alpha) (\mathscr D
_{q}g)(\alpha),\qquad \alpha\in \mathbb R, \quad N\ge 0, \] where $\bf u$ is a
$q$-classical linear functional and $\mathscr D _{q}$ is the $q$-derivative
operator.
  We obtain some algebraic properties of these polynomials such as an explicit
representation, a five-term recurrence relation as well as a second order
linear $q$-difference holonomic equation fulfilled by such polynomials.
  We present an analysis of the behaviour of its zeros function of the mass
$N$. In particular, we in the exact values of $N$ such that the smallest
(respectively, the greatest) zero of the studied polynomials is located outside
of the support of the measure.
  We conclude this work considering two examples.

Classical Analysis and ODEs