  In this paper, we examined the viability bounds of a higher derivative
$f(R,\Box R, T)$ theory through analyzing energy conditions (where $R$ and $T$
are the Ricci scalar and trace of energy momentum tensor, respectively). We
take flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime coupled with ideal
configurations of matter content. We consider three different realistic models
of this gravity, that could be utilized to understand the stability of
cosmological solutions. After constructing certain bounds mediated by energy
conditions, more specifically weak energy condition, we discuss viable zones of
the under considered modified models in an environment of recent estimated
numerical choices of the cosmic parameters.
