Which differintegration?

IEE Proceedings Vision, Image & Signal Processing, vol. 152, nº 6

Despite the great advances in the theory and applications of fractional calculus, some topics remain unclear making a systematic use difficult. In this paper the fractional differintegration definition problem is studied from a systems point of view. Both local (Grünwald-Letnikov) and global (convolutional) definitions are considered. It is shown that the Cauchy formulation should be adopted since it is coherent with usual practice in signal processing and control applications.