State space modeling of fractional differential equations and the initial condition problem

摘要

This paper presents a state space representation of FDEs based on two complementary models: a simulation state space model with fractional order integrators, and a state space model for each integrator. The resulting complete model is an ODE which is infinite dimensional. With these definitions of the FDE model and of its state variables, the initial condition problem becomes elementary and no longer connected to the definition of the fractional order derivatives.