Complex-Order Distributions

Abstract

This paper develops the concept of the complex order-distribution. This is a continuum of fractional differintegrals whose order is complex. Two types of complex order-distributions are considered, uniformly distributed and Gaussian distributed. It is shown that these basis distributions can be summed to approximate other complex order-distributions. Conjugated differintegrals are an essential analytical tool applied in this development due to their associated real time-responses. An example is presented to demonstrate the complex order-distribution concept. This work enables the generalization of fractional system identification to allow the search for complex order-derivatives that may better describe real time behaviors.