Abstract
This chapter presents the use of models of non-integer (fractional) order for modeling of dynamic systems. Ultracapacitors have been presented as systems with these types of dynamics. Their internal structure and energy storage method were thoroughly analyzed. The diffusion process used in their operation has in their mathematical description derivatives of non integer order, which confirms the legitimacy of using models of non integer order to describe their dynamics. As part of this chapter, various models of ultracapacitors used to model their dynamics in time and frequency domain are presented. The presented transmittance models have been thoroughly discussed and confirmed by their comparison with properties observed in laboratory experiments with the ultracapacitors. The last chapter presents a fractional order neural network, which, using the differences of the non integer order, despite its simple structure, allows for accurate mapping of the process of charging and discharging ultracapacitors.
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