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Initialization of Riemann-Liouville and Caputo Fractional Derivatives

[+] Author Affiliations
Jean-Claude Trigeassou, Alain Oustaloup

University of Bordeaux, Bordeaux, France

Nezha Maamri

University of Poitiers, Poitiers, France

Paper No. DETC2011-47633, pp. 219-226; 8 pages
doi:10.1115/DETC2011-47633
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME

abstract

Riemann-Liouville and Caputo fractional derivatives are fundamentally related to fractional integration operators. Consequently, the initial conditions of fractional derivatives are the frequency distributed and infinite dimensional state vector of fractional integrators. The paper is dedicated to the estimation of these initial conditions and to the validation of the initialization problem based on this distributed state vector. Numerical simulations applied to Riemann-Liouville and Caputo derivatives demonstrate that the initial conditions problem can be solved thanks to the estimation of the initial state vector of the fractional integrator.

Copyright © 2011 by ASME

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