  We consider the paradigm of an overdamped Brownian particle in a potential
well, which is modulated through an external protocol, in the presence of
stochastic resetting. Thus, in addition to the short range diffusive motion,
the particle also experiences intermittent long jumps which reset the particle
back at a preferred location. Due to the modulation of the trap, work is done
on the system and we investigate the statistical properties of the work
fluctuations. We find that the distribution function of the work typically, in
asymptotic times, converges to a universal Gaussian form for any protocol as
long as that is also renewed after each resetting event. When observed for a
finite time, we show that the system does not generically obey the Jarzynski
equality which connects the finite time work fluctuations to the difference in
free energy, albeit a restricted set of protocols which we identify herein. In
stark contrast, the Jarzynski equality is always fulfilled when the protocols
continue to evolve without being reset. We present a set of exactly solvable
models, demonstrate the validation of our theory and carry out numerical
simulations to illustrate these findings. Finally, we have pointed out possible
realistic implementations for resetting in experiments using the so-called
engineered swift equilibration.
