  Motivated by a recent work of one of us [1], we extend it by using quantum
(or entropy) corrected new agegraphic dark energy in the Brans-Dicke cosmology.
The correction terms are motivated from the loop quantum gravity which is one
of the competitive theories of quantum gravity. Taking the non-flat background
spacetime along with the conformal age of the universe as the length scale, we
derive the dynamical equation of state of dark energy and the deceleration
parameter. An important consequence of this study is the phantom divide
scenario with entropy-corrected new agegraphic dark energy. Moreover, we assume
a system of dark matter, radiation and dark energy, while the later interacts
only with dark matter. We obtain some essential expressions related with dark
energy dynamics. The cosmic coincidence problem is also resolved in our model.
