  Random flights (also called run-and-tumble walks or transport processes)
represent finite velocity random motions changing direction at any Poissonian
time. These models in d-dimension, can be studied giving a general formulation
of the problem valid at any spatial dimension. The aim of this paper is to
extend this general analysis to time-fractional processes arising from a
non-local generalization of the kinetic equations. The probabilistic
interpretation of the solution of the time-fractional equations leads to a
time-changed version of the original transport processes. The obtained results
provides a clear picture of the role played by the time-fractional derivatives
in this kind of random motions. They displayed an anomalous behavior and are
useful to describe several complex systems arising in statistical physics and
biology. In particular, we focus on the one-dimensional random flight, called
telegraph process, studying the time-fractional version of the classical
telegraph equation and providing a suitable interpretation of its stochastic
solutions.
