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We consider a cosmological model of non-minimal derivative coupling (NMDC) togravity with holographic effect from Bekenstein-Hawking entropy using Hubblehorizon IR cutoff. Holographic parameter $c$ is constant in a range, $0 \leq c< 1$. NMDC effect allows gravitational constant to be time-varying. Definitionof holographic density include time-varying part of the gravitational constant.NMDC part reduces strength of gravitational constant for $\k > 0$ and oppositefor $\k < 0$. The holographic part enhances gravitational strength. We usespectral index and tensor-to-scalar ratio to test the model against CMBconstraint. Number of e-folding is chosen to be $N \geq 60$. Potentials, $V =V_0 \phi^n $ with $n = 2, 4$, and $V = V_0 \exp{(-\beta \phi)}$ are considered.Combined parametric plots of $\k$ and $\phi$ show that the allowed regions ofthe power spectrum index and of the tensor-to-scalar ratio are not overlapping.NMDC inflation is ruled out and the holographic NMDC inflation is also ruledout for $0 < c < 1$. NMDC significantly changes major anatomy of the dynamics,i.e. it gives new late-time attractor trajectories in acceleration regions. Theholographic part clearly affects pattern of trajectories. However, for theholographic part to affect shape of the acceleration region, the NMDC fieldmust be in presence. To constrain the model at late time, variation ofgravitational constant is considered. Gravitational-wave standard sirens andsupernovae data give a constraint, $\dot{G}/G|_{t_0} \lesssim 3\times10^{-12}\, \text{year}^{-1}$ \cite{Zhao:2018gwk} which, for this model, results in $10^{-12} \, \text{year}^{-1} \, \gtrsim \, {- \kappa}\dot{\phi}\ddot{\phi}/{M^2_{\p}}\,. $ Positive $\k$ is favored and greater$c^2$ results in lifting up lower bound of $\k$.

Cosmology in holographic non-minimal derivative coupling theory: constraints from inflation and variation of gravitational constant