On self-consistent operators with application to operators of fractional order

Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009

Volumn 4, Issue PART B, 2010, Pages 1069-1075

  Lorenzo, Carl F ^a   Hartley, Tom T ^b  

^a NASA GLENN RESEARCH CENTER   (United States)

^b UNIVERSITY OF AKRON   (United States)

Author keywords

Caputo derivative; Continuation function; Initialization function; Riemann liouville integral

Indexed keywords

CAPUTO DERIVATIVE; CAPUTO DERIVATIVES; CAPUTO FRACTIONAL DERIVATIVES; CONTINUATION FUNCTION; FRACTIONAL INTEGRALS; FRACTIONAL ORDER; RIEMANN INTEGRAL; RIEMANN-LIOUVILLE INTEGRAL; SELF-CONSISTENCY; TIME VARYING;

LAPLACE TRANSFORMS; WAVELET TRANSFORMS;

TIME VARYING SYSTEMS;

EID: 77953691814     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2009-86730     Document Type: Conference Paper

References (8)

1. Lorenzo, Carl F., and Hartley, Tom T., "Initialization of Fractional-Order Operators and Fractional Differential Equations" Special Issue on Fractional Calculus of ASME Journal of Computational and Nonlinear Dynamic, Special Issue on Discontinuous and Fractional Dynamical Systems, Vol. 3, No. 2, 020201, April 2008.
2. nd Ed., , ISBN-13:9780070108738, ISBN0070108730, McGraw Hill Book Co, New York, NY, 1960.
3. Podlubny, Igor, Fractional Differential Equations:. An Introduction to Fractional Derivatives, Fractional Differential Equations, to methods of their Solution and some of their Applications. Mathematics in Science and Engineering, Vol. 198, Academic Press, 1999.
4. Caputo, M, Linear model of dissipation whose Q is almost frequency independent-II Geophy. J. R. Astr. Soc. vol. 13, 1967 pp529-539.
5. Caputo, M. Elastica e Dissipaszione, Zanicelli, Bolgna, 1969.
6. Achar, B. N. Narahari, Lorenzo, Carl F., and Hartley, Tom T., "Initialization and the Caputo Fractional Derivative" NASA TM-2003-212482, July 2003.
7. Achar, B. N. Narahari, Lorenzo, Carl F., and Hartley, Tom T., "Initialization Issues of the Caputo Fractional Derivative", Proceedings of DETC/CIE 2005, ASME Int. Design Engineering Technical Conference, DETC2005- 84348, Long Beach Ca., Sept. 24-28, 2005.
8. Achar, B. N. Narahari, Lorenzo, Carl F., and Hartley, Tom T., "The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equations" pp.27-42, in - Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Ed. J. Sabatier, O. P. Agrwal, J. A. Tenreiro Machado, ISBN 978-1-4020-6041-0 (HB), Springer, 2007.