An extremely fast and accurate fractional order differentiator

Abstract

Unlike their integer order counterparts, fractional order differentiation is a non-local operation and its computation requires evaluating nested loops over the history of the operated functions. This causes the process to be terribly slow when software based implementations are made using interpreted languages like Python, MATLAB®, etc. The present work demonstrates the development of a fast yet accurate fractional order differentiator that can be used as a standard Python function. Its performance and accuracy are compared with those of the other standard tools currently available in the market. Given its importance in the relevant domains, the present implementation is made available as a free software.