Research Papers

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

[+] Author and Article Information
Tom T. Hartley

University of Akron,
Akron, OH 44325-3904
e-mail: thartley@uakron.edu

Carl F. Lorenzo

NASA Glenn Research Center,
Cleveland, OH 44135
e-mail: Carl.F.Lorenzo@nasa.gov

Jean-Claude Trigeassou

University of Bordeaux 1,
Talence Cedex, 33405, France
e-mail: jean-claude.trigeassou@ims-bordeaux.fr

Nezha Maamri

LIAS ENSIP University of Poitiers,
Poitiers Cedex, 86000France
e-mail: nezha.maamri@univ-poitiers.fr

Contributed by the Design Engineering Division for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received October 1, 2012; final manuscript received February 1, 2013; published online June 10, 2013. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(4), 041014 (Jun 10, 2013) (7 pages) Paper No: CND-12-1164; doi: 10.1115/1.4023865 History: Received October 01, 2012; Revised February 01, 2013

Proper initialization of fractional-order operators has been an ongoing problem, particularly in the application of Laplace transforms with correct initialization terms. In the last few years, a history-function-based initialization along with its corresponding Laplace transform has been presented. Alternatively, an infinite-dimensional state-space 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 fractional-order operators are equivalent and that the associated Laplace transforms yield the correct initialization terms and can be used in the solution of fractional-order differential equations.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Fig. 1

History function and initialization function for a fractional operator and the system initialization response




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In