  We analyze two models of subdiffusion with stochastic resetting. Each of them
consists of two parts: subdiffusion based on the continuous-time random walk
(CTRW) scheme and independent resetting events generated uniformly in time
according to the Poisson point process. In the first model the whole process is
reset to the initial state, whereas in the second model only the position is
subject to resets. The distinction between these two models arises from the
non-Markovian character of the subdiffusive process. We derive exact
expressions for the two lowest moments of the full propagator, stationary
distributions, and first hitting times statistics. We also show, with an
example of a constant drift, how these models can be generalized to include
external forces. Possible applications to data analysis and modeling of
biological systems are also discussed.
