  Recent discovery of fast blue optical transients (FBOTs) as a new class of
energetic transient sources can shed light on the long-standing problem of
supernova-long gamma-ray burst connections. A distinctive feature of such
objects is the presence of modestly relativistic outflows which place them in
between the non-relativistic and relativistic supernovae-related events. Here
we present the results of kinetic particle-in-cell and Monte Carlo simulations
of particle acceleration and magnetic field amplification by shocks with the
velocities in the interval between 0.1 and 0.7 c. These simulations are needed
for the interpretation of the observed broad band radiation of FBOTs. Their
fast, mildly to moderately relativistic outflows may efficiently accelerate
relativistic particles. With particle-in-cell simulations we demonstrate that
synchrotron radiation of accelerated relativistic electrons in the shock
downstream may fit the observed radio fluxes. At longer timescales, well beyond
those reachable within a particle-in-cell approach, our nonlinear Monte Carlo
model predicts that protons and nuclei can be accelerated to petaelectronvolt
(PeV) energies. Therefore, such fast and energetic transient sources can
contribute to galactic populations of high energy cosmic rays.
