An explicit numerical scheme for solving fractional order compartment models from the master equations of a stochastic process

We derive the generalized master equations for a stochastic process representing populations entering, leaving, or waiting in compartments at discrete times. This discrete time compartment model limits to a fractional order continuous time compartment model for a particular choice of waiting time distribution and the appropriate limiting process. We demonstrate that the discrete time master equations can be used to provide an explicit numerical method that can be employed for solving the fractional order compartment equations. The advantage of this approach is that the numerical scheme has a physical interpretation, it is stable, and it is easy to implement. The method can be applied to a wide class of fractional order compartment model equations that arise in a broad range of applications.