  In this paper, the cosmological implications of the Power Law Entropy
Corrected Holographic Dark Energy (PLECHDE) and the Logarithmic Entropy
Corrected Holographic Dark Energy (LECHDE) models in the context of Brans-Dicke
(BD) cosmology for both non-interacting and interacting DE and Dark Matter (DM)
are studied. As the system infrared cut-off, we choose the recently proposed
Granda-Oliveros cut-off, which contains a term proportional to the first time
derivative of the Hubble parameter and one term proportional to $H^2$, i.e. the
Hubble parameter squared. We obtain the expressions of three quantities, i.e.
the Equation of State (EoS) parameter $\omega_D$, the deceleration parameter
$q$ and the evolutionary form of the energy density parameter $\Omega'_D$ of
the PLECHDE and LECHDE models in a non-flat Universe for non-interacting and
interacting DE and DM as well. Moreover, we investigate the limiting cases
corresponding to: a) absence of entropy corrections; b) Einstein's gravity; and
c) concomitantly absence of entropy corrections and Einstein's gravity.
Furthermore, we consider the limiting case corresponding to the Ricci scale,
which is recovered for some particular values of the parameters characterizing
the Granda-Oliveros scale. We also study the statefinder diagnostic and the
cosmographic parameters for both models considered in this work.
