  This paper studies the viable regions of some cosmic models in a higher
derivative $f(R,\square R, T)$ theory with the help of energy conditions (where
$R$ and $T$ are the Ricci scalar, and trace of energy momentum tensor,
respectively). For this purpose, we assume a flat
Friedmann-Lema\^{i}tre-Robertson-Walker metric which is assumed to be filled
with perfect fluid configurations. We take two distinct realistic models, that
might be helpful to explore stable regimes of cosmological solutions. After
taking some numerical values of cosmic parameters, like crackle, snap, jerk
(etc) as well as viable constraints from energy conditions, the viable zones
for the under observed $f(R,\square R, T)$ models are examined.
