The error incurred in using the Caputo-derivative Laplace-transform

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

Volumn 4, Issue PART A, 2010, Pages 271-278

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

^a UNIVERSITY OF AKRON   (United States)

^b NASA GLENN RESEARCH CENTER   (United States)

Author keywords

Caputo derivative; Fractional order systems; Initialization; Rho function

Indexed keywords

CAPUTO DERIVATIVES; FRACTIONAL DERIVATIVES; FRACTIONAL-ORDER SYSTEMS; INITIALIZATION PROBLEM;

WAVELET TRANSFORMS;

DIFFERENTIAL EQUATIONS;

EID: 77953704972     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2009-87648     Document Type: Conference Paper

References (13)

1. M. Fukunaga,"On initial value problems in fractional differential equations," Int. J. Appl. Mathematics, Vol 9, 219-236, 2002.
2. M. Fukunaga, and N. Shimizu,"Role of prehistories in the initial value problems of fractional viscoelastic equations," Nonlinear Dynamics, Vol 38, 207-220, 2004.
3. Tom T. Hartley and Carl F. Lorenzo,"Dynamics and Control of Initialized Fractional-Order Systems," Nonlinear Dynamics, vol 29, nos 1-4, pp 201-233, July 2002.
4. Tom T. Hartley and Carl F. Lorenzo,"Application of the Incomplete Gamma Functions to the Initialization of Fractional-order Systems," ASME J. of Comp. and Nonlinear Dynamics, vol 3, no 2, pp 021101-1 to 021101-9, April 2008.
5. Tom T. Hartley and Carl F. Lorenzo,"The Initialization Response of Linear Fractional-order Systems with Constant History Function," submitted to Proceedings of IDETC/CIE 2009, ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, August 30-September 2, 2009a, San Diego, CA, USA.
6. Tom T. Hartley and Carl F. Lorenzo,"The Initialization Response of Linear Fractional-order Systems with a Ramp History Function," submitted to Proceedings of IDETC/CIE 2009, ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, August 30-September 2, 2009b, San Diego, CA, USA.
7. Carl. F. Lorenzo and Tom T. Hartley,"Initialization of Fractional Differential Equations," ASME Journal of Computational and Nonlinear Dynamics, vol 3, no 2, pp 021103-1 to 021103-6, April 2008.
8. Keith B. Oldham and Jerome Spanier, The Fractional Calculus, Academic Press, 1974.
9. Manuel D. Ortigueira, Fernando J. Coito,"Initial Conditions: What Are We Talking About?" IFAC Workshop on Fractional Derivatives and Application, Ankara, Turkey, 2008.
10. Igor Podlubny, Fractional Differential Equations, Academic Press, 1999.
11. G.E. Roberts and H. Kaufman, Table of Laplace Transforms, W.B. Saunders Co., 1966.
12. Jocelyn Sabatier, Mathieu Merveillaut, Rachid Malti, Alain Oustaloup,"On a Representation of Fractional Order Systems: Interests for The Initial Condition Problem," IFAC Workshop on Fractional Derivatives and Application, Ankara, Turkey, 2009.
13. Jerome Spanier and Keith B. Oldham, An Atlas of Functions, Hemisphere Publishing Corporation, New York, 1987.