Fractional-Order Learning Systems

From the inaugural steps of McCulloch and Pitts to put forth a composition for an electrical brain, that combined with the conception of an adaptive leaning mechanism by Widrow and Hoff has given rise to the phenomena of intelligent machines, machine learning techniques have gained the status of a miracle solution in a myriad of scientific fields. At the heart of these techniques lies iterative optimisation processes that are derived based on first, and in some cases, second-order derivatives. This manuscript, however, aims to expand the mentioned framework to that of using fractional-order derivatives. The entire format of adaptation is revised form the perspective of fractional-order calculus and the appropriate framework for taking full advantage of the fractional-order calculus in learning and adaptation paradigms is formulated. For rigour, the structure of behavioural analysis and performance prediction of this novel class of learning machines is also forged.