  In this work we consider intermediate inflation in context of the Generalized
Non-Minimal Derivative Coupling (GNMDC) model. In this model, inflation is
driven by a canonical scalar field, which is coupled not only to gravity but
also to the derivative of the scalar field. GNMDC introduces new dynamics and
features during the inflationary epoch. We find inflationary solutions with the
power law scalar field for the power law coupling function and we find the
inflaton potential that generate intermediate expansion of the scale factor.
Also, we discuss background equations in the high friction limit and we obtain
constraints on the parameters of our model. Furthermore, we investigate the
cosmological perturbations in the slow roll approximation within the GNMDC
model, and we compute the scalar and tensor spectral index and tensor-to-scalar
ratio in the intermediate inflation. We also compare results of this model with
the observational signatures that can be used to test this model in the cosmic
microwave background radiation. Overall, we draw condition for inflaton
potential that accelerated expansion continue during the slow roll inflation.
Numerically we consider power spectrum and spectral index for scaler and tensor
modes in intermediate inflation in the high friction limit. Moreover, based on
Planck 2018 data, we find constraints on the parameters of the model. We show
that intermediate inflation in GNMDC is successful in evaluation and
explanation of the background and perturbational quantities of observational
cosmology.
