  In this paper, we study the main cosmological properties of the classical
Friedmann equations in the case of homogeneous and isotropic
Friedmann-Robertson-Walker Universe and we also generalized the expression of
the Friedmann equation in the case of Loop Quantum Cosmology (LQC). Considering
the $M_{35}$-model, we found the solutions of the equations considered for two
particular cases, i.e. $Q=0$ (i.e., the de Sitter solution) and $Q>0$.
Moreover, we considered and studied two exact cosmological solutions of the
$M_{35}$-model, in particular the power-law and the exponential ones.
Futhermore, we also considered a third more complicated case and we derived the
solution for an arbitrary function of the time $f\left(t\right)$. A scalar
field description of the model is presented by constructing its
self-interacting potential.
