  Understanding the high-energy emission processes and variability patterns are
two of the most challenging research problems associated with relativistic
jets. In particular, the long-term (months-to-years) flux variability at very
high energies (VHE, $>$50 GeV) has remained an unexplored domain so far. This
is possibly due to the decreased sensitivity of the Fermi Large Area Telescope
(LAT) above a few GeV, hence low photon statistics, and observing constraints
associated with the ground-based Cherenkov telescopes. This paper reports the
results obtained from the 0.05$-$2 TeV Fermi-LAT data analysis of a sample of
29 blazars with the primary objective to explore their months-to-year long VHE
flux variability behavior. This systematic search has led to, for the first
time, the detection of significant flux variations in 5 blazars at $>$99\%
confidence level, whereas, 8 of them exhibit variability albeit at a lower
confidence level ($\sim$95\%-99\%). A comparison of the 0.05$-$2 TeV flux
variations with that observed at 0.1$-$50 GeV band has revealed similar
variability behavior for most of the sources. However, complex variability
patterns that are not reflected contemporaneously in both energy bands were
also detected, thereby providing tantalizing clues about the underlying
radiative mechanisms. These results open up a new dimension to unravel the VHE
emission processes operating in relativistic jets, hence sowing the seeds for
their future observations with the upcoming Cherenkov Telescope Array.
