Fractional heterogeneous telegraph processes: Interplay between heterogeneity, memory, and stochastic resetting.

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Fractional heterogeneous telegraph processes are considered in the framework of telegrapher's equationsaccompanied by memory effects. The integral decomposition method is developed for the rigorous treating of the problem. Exact solutions for the probability density functions and the mean squared displacements are obtained. A relation between the fractional heterogeneous telegrapher's equationand the corresponding Langevin equationhas been established in the framework of the developed subordination approach. The telegraph process in the presence of stochastic resetting has been studied, as well. An exact expression for both the nonequilibrium stationary distributions/states and the mean squared displacements are obtained.