In time a system is characterized by differential equation, how the parameter of a systems are iterativelly estimated if the derivative involved are of fraction order?
If you are interested in signal processing based techniques, use Haar Wavelets based methods.There are a number of papers on the topic Haar Fractional Method.
It is not easy to give a general response. It would be better to have a concrete equation to deal with just to see how to separate a known, or measurable regressor, ( measurements/data, etc.) and a parameter or parameter vector to be estimated by some recursive algorithm.