  In a very recent paper, the current authors (arXiv:gr-qc/1609.01477) have
proposed and analyzed in detail the logarithmic form of Brans-Dicke scalar
field $\phi$ as $\phi \propto ln(\alpha+\beta a)$, where $\alpha$ and $\beta$
are positive constants, to alleviate the problems of interacting holographic
dark energy models in Brans-Dicke theory. In this paper, the cosmological
evolution of a new agegraphic dark energy (NADE) model within the framework of
Friedmann-Robertson-Walker Universe is analyzed with the same form of scalar
field in Brans-Dicke theory. We derive the equation of state parameter $w_D$
and deceleration parameter $q$ of NADE model. It is observed that
$w_D\rightarrow -1$ when $a\rightarrow \infty$, i.e., the NADE mimics
cosmological constant in the late time evolution. Indeed, due to the assumption
of logarithmic form of Brans-Dicke scalar field the NADE in Brans-Dicke theory
behaves like NADE in general relativity in the late time evolution. The NADE
model shows a phase transition from matter dominated phase in early time to
accelerated phase in late time. We further extend NADE model by including the
interaction between dark matter and NADE. In this case, $w_D$ definitely
crosses the phantom divide line ($w_D=-1$) in the late time evolution. The
phase transition from matter dominated to NADE dominated phase may be achieved
at early stage in interacting model. Further, we show that the interacting NADE
model resolves the cosmic coincidence problem as the energy density ratio may
evolve sufficiently slow at present.
