  We report on the time dependent solutions of the $q-$generalized
Schr\"odinger equation proposed by Nobre et al. [Phys. Rev. Lett. 106, 140601
(2011)]. Here we investigate the case of two free particles and also the case
where two particles were subjected to a Moshinsky-like potential with time
dependent coefficients. We work out analytical and numerical solutions for
different values of the parameter $q$ and also show that the usual
Schr\"odinger equation is recovered in the limit of $q\rightarrow 1$. An
intriguing behavior was observed for $q=2$, where the wave function displays a
ring-like shape, indicating a bind behavior of the particles. Differently from
the results previously reported for the case of one particle, frozen states
appear only for special combinations of the wave function parameters in case of
$q=3$.
