  By assuming the spatially flat~FLRW line-element and employing the
Hamiltonian formalism, a noncommutative (NC) setting of the Brans-Dicke (BD)
theory is introduced. We investigate gravity-driven acceleration and kinetic
inflation in this NC BD cosmology. Despite to the commutative case, in which
both the scale factor and BD scalar field are obtained in power-law forms (in
terms of the cosmic time), in our herein NC model, we see that the power-law
scalar factor is multiplied by a dynamical exponential warp factor. This warp
factor depends on not only the NC parameter but also the momentum conjugate
associated to the BD scalar field. For very small values of this parameter, we
obtain an appropriate inflationary solution, which can overcome the problems
within the standard BD cosmology in a more efficient manner. Moreover, we see
that a graceful exit from an early acceleration epoch towards a decelerating
radiation epoch is provided. For late times, due to the presence of the NC
parameter, we obtain a zero acceleration epoch, which can be interpreted as the
coarse-grained explanation.
