  In this paper, we introduce a noncommutative version of the Brans-Dicke (BD)
theory and obtain the Hamiltonian equations of motion for a spatially flat
Friedmann--Lema\^{\i}tre--Robertson--Walker universe filled with a perfect
fluid. We focus on the case where the scalar potential as well as the ordinary
matter sector are absent. Then, we investigate gravity-driven acceleration and
kinetic inflation in this noncommutative BD cosmology. In contrast to the
commutative case, in which the scale factor and BD scalar field are in a
power-law form, in the noncommutative case the power-law scalar factor is
multiplied by a dynamical exponential warp factor. This warp factor depends on
the noncommutative parameter as well as the momentum conjugate associated to
the BD scalar field. We show that the BD scalar field and the scale factor
effectively depend on the noncommutative parameter. For very small values of
this parameter, we obtain an appropriate inflationary solution, which can
overcome problems within BD standard cosmology in a more efficient manner.
Furthermore, a graceful exit from an early acceleration epoch towards a
decelerating radiation epoch is provided. For late times, due to the presence
of the noncommutative parameter, we obtain a zero acceleration epoch, which can
be interpreted as the coarse-grained explanation.
