  The present article investigates the possibility of reconstruction of the
generic function in $F(\mathcal{R},T)$ gravitational theory by considering some
well-known cosmological bouncing models namely exponential evaluation,
oscillatory, power law and matter bounce model, where $\mathcal{R}$ and $T$ are
Ricci scalar and trace of energy-momentum tensor, respectively. Due to the
complexity of dynamical field equations, we propose some ansatz forms of
function $F(\mathcal{R},T)$ in perspective models and examine that which type
of Lagrangian is capable to reproduce bouncing solution via analytical
expression. It is seen that for some cases of exponential, oscillatory and
matter bounce models, it is possible to get analytical solution while in other
cases, it is not possible to achieve exact solutions so only complementary
solutions can be discussed. However, for power law model, all forms of generic
function can be reconstructed analytically. Further, we analyze the energy
conditions and stability of these reconstructed cosmological bouncing models
which have analytical forms. It is found that these models are stable for
linear forms of Lagrangian only but the reconstructed solutions for power law
are unstable for some non-linear forms of Lagrangian.
