  This paper presents a noncommutative (NC) version of an extended
S\'{a}ez-Ballester (SB) theory. Concretely, considering the spatially flat
Friedmann-Lema\^{\i}tre-Robertson-Walker~(FLRW) metric, we propose an
appropriate dynamical deformation between the conjugate momenta and applying
the Hamiltonian formalism, obtain deformed equations of motion. In our model,
the NC parameter appears linearly in the deformed Poisson bracket and the
equations of the NC SB cosmology. When it goes to zero, we get the
corresponding commutative counterparts. Even by restricting our attention to a
particular case, where there is neither an ordinary matter nor a scalar
potential, we show that the effects of the noncommutativity provide interesting
results: applying numerical endeavors for very small values of the NC
parameter, we show that (i) at the early times of the universe, there is an
inflationary phase with a graceful exit, for which the relevant nominal
condition is satisfied; (ii) for the late times, there is a zero acceleration
epoch. By establishing an appropriate dynamical framework, we show that the
results (i) and (ii) can be obtained for many sets of the initial conditions
and the parameters of the model. Finally, we indicate that, at the level of the
field equations, one may find a close resemblance between our NC model and the
Starobinsky inflationary model.
