Title: Fractional compound Poisson processes with multiple internal states,
Abstract: For the particles undergoing the anomalous diffusion with different waiting
time distributions for different internal states, we derive the Fokker-Planck
and Feymann-Kac equations, respectively, describing positions of the particles
and functional distributions of the trajectories of particles; in particular,
the equations governing the functional distribution of internal states are also
obtained. The dynamics of the stochastic processes are analyzed and the
applications, calculating the distribution of the first passage time and the
distribution of the fraction of the occupation time, of the equations are
given.