Optimal first arrival times in L\'evy flights with resetting

We consider diffusive motion of a particle performing a random walk with L\'evy distributed jump lengths and subject to resetting mechanism bringing the walker to an initial position at uniformly distributed times. In the limit of infinite number of steps and for long times, the process converges to a super-diffusive motion with replenishment. We derive formula for a mean first arrival time (MFAT) to a predefined target position reached by a meandering particle and analyze efficiency of the proposed searching strategy by investigating criteria for an optimal (a shortest possible) MFAT.