  In this paper we study finite velocity planar random motions with an infinite
number of possible directions, where the number of changes of direction is
randomized by means of an inhomogeneous fractional Poisson distribution. We
first discuss the properties of the distributions of the generalized fractional
inhomogeneous Poisson process. Then we show that the explicit probability law
of the planar random motions where the number of changes of direction is
governed by this fractional distribution can be obtained in terms of
Mittag-Leffler functions. We also consider planar random motions with random
velocities obtained from the projection of random flights with Dirichlet
displacements onto the plane, randomizing the number of changes of direction
with a suitable adaptation of the fractional Poisson distribution.
