First-passage times for generalized heterogeneous telegrapher's processes.

We consider two different fractional generalizations of the heterogeneous telegrapher's process with and without stochastic resetting. Both governing fractional heterogeneous telegrapher's equations can be obtained from the corresponding standard heterogeneous telegrapher's equations by using the subordination approach. The first-passage time problems are solved analytically for both models by finding the survival probabilities, the first-passage time densities, and the mean first-passage times. We showed that for both cases there are optimal resetting rates for which the mean first-passage times are minimal. The present work carries implications toward our understanding of anomalous diffusion and random search in heterogeneous media.