  We introduce a non-homogeneous fractional Poisson process by replacing the
time variable in the fractional Poisson process of renewal type with an
appropriate function of time. We characterize the resulting process by deriving
its non-local governing equation. We further compute the first and second
moments of the process. Eventually, we derive the distribution of arrival
times. Constant reference is made to previous known results in the homogeneous
case and to how they can be derived from the specialization of the
non-homogeneous process.
