Equivalence of History Function Based and Infinite Dimensional State Initializations for Fractional Order Operators

Abstract

Proper initialization of fractionalorder operators has been an ongoing problem, particularly in the application of Laplace transforms with correct initialization terms. In the last few years, a historyfunctionbased initialization along with its corresponding Laplace transform has been presented. Alternatively, an infinitedimensional statespace representation along with its corresponding Laplace transform has also been presented. The purpose of this paper is to demonstrate that these two approaches to the initialization problem for fractionalorder operators are equivalent and that the associated Laplace transforms yield the correct initialization terms and can be used in the solution of fractionalorder differential equations.