Physical interpretation and initialization of the fractional integrator

The equivalence between the infinite RC transmission line and the fractional order integrator is analyzed in the paper. This equivalence is used to demonstrate that the integrator infinite state model corresponds to the spatial Fourier transform of the RC line diffusive model. A direct consequence is the correspondence between integrator initialization in the time domain and RC line initialization in the spatial domain. Practical integrator initialization can be only approximated: a solution to this basic problem is provided by an observer based technique.