  Classical Be stars, regardless of spectral subtype, display multiperiodic
light modulations in the frequency range 0.1-12 d$^{-1}$, when observed with
high-cadence and long duration. This behaviour is attributed to non-radial
pulsations and/or rotation of the Be star. The main goal of this work is to
investigate the fast photometric variability of the optical counterparts to
Be/X-ray binaries and compare the general patterns of such variability with the
Galactic population of classical Be stars. We analyzed 21 sources with TESS.
High-cadence photometry with two ground-based telescopes was also performed for
15 sources. Standard Fourier analysis and least-squares fitting methods were
employed in the frequency analysis. All sources exhibit intra-night light
variations with intensity variations of 0.01-0.06 mag in the ground-based
observations and up to 5% in flux in TESS observations. This variability
manifests itself as multi-periodic signals in the frequency range 0.2-12
d$^{-1}$. We find that the patterns of variability of the Be stars in Be/X-ray
binaries agree with that of classical early-type Be stars in terms of the
general shape of the periodograms. Based on the general shape and number of
peaks in the periodograms, Be/X-ray binaries can be classified into different
types. The most common case is the presence of groups of closely-spaced
frequencies (67%), followed by sources that exhibit isolated signals (18%). The
remaining type of sources displays frequency spectra characterized by a mixed
pattern of stochastic variability and high-frequency peaks. This study reveals
that short-term optical photometric variability is a very common, if not
ubiquitous, feature intrinsic to the Be optical companions in Be/X-ray
binaries. This variability is mainly attributed to pulsations that originate in
the stellar interior.
