  This study aims to explore the Garcia-Salcedo ghost dark energy and
generalized ghost dark energy models in the context of
$f(\mathrm{R},\mathrm{T^2})$ theory, where $\mathrm{R}$ is the Ricci scalar and
$\mathrm{T^2}$ is the self-contraction of stress-energy tensor. We investigate
the non-interacting case only corresponding to flat Friedmann-Robertson-Walker
universe. We reconstruct the corresponding $f(\mathrm{R},\mathrm{T^2})$ gravity
models using the considered dark energy models by taking two particular models
of this gravity. The stability analysis is performed for all the cases. The
behavior of the equation of state parameter is also checked. It is found that
some of the reconstructed $f(\mathrm{R},\mathrm{T^2})$ models successfully
describe both the phantom and quintessence epochs of the universe, which
support the current cosmic accelerated expansion. This exploration reveals the
intricate connections between dark energy models and modified gravitational
theory, providing significant understanding into the dynamics of the cosmos on
a large scale.
