The caputo fractional derivative: Initialization issues relative to fractional differential equation

Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering

Volumn , Issue , 2007, Pages 27-42

  Achar, B N Narahari ^a   Lorenzo, Carl F ^b   Hartley, Tom T ^c  

^a University of Memphis   (United States)

^b NASA GLENN RESEARCH CENTER   (United States)

^c UNIVERSITY OF AKRON   (United States)

Author keywords

Caputo fractional derivatives; initialization issues

Indexed keywords

EID: 77953710313     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4020-6042-7_3     Document Type: Chapter

References (13)

1. Lorenzo CF, Hartley TT (2000) Initialized fractional calculus. Int. J. Appl. Math. 3(3):249-265.
2. Lorenzo CF, Hartley TT (2001) Initialization in Fractional Order Systems, in: Proceedings of the European Control Conference, Porto, Portugal pp. 1471-1476.
3. Oldham KB, Spanier J (1974) The Fractional Calculus-Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press, New York.
4. Miller KS, Ross B (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York.
5. Samko SG, Kilbas AA, Marichev OI (1993) Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, Philadelphia, PA.
6. Podlubny L (1999) Fractional Differential Equations. Academic Press, SanDiego, CA.
7. Lorenzo CF, Hartley TT (1998) Initialization, Conceptualization, and Application in the Generalized Fractional Calculus. NASA TM-1998.
8. Caputo M (1969) Elasticita e Dissipazione. Zanichelli, Bologna.
9. Caputo M (1967) Linear Model of dissipation whose Q is almost frequency independent-II. Geophys. J. R. Astron. Soc. 13:529-539.
10. Gorenflo R, Mainardi F (1997) Fractional calculus, integral and differential equations of fractional order in: Fractals and Fractional Calculus in Continuum Mechanics. Carpenteri, A, Mainardi, F (eds.), Springer, New York.
11. Achar BNN, Lorenzo CF, Hartley T (2003) Initialization and the Caputo Fractional Derivative. NASA TM-2003.
12. Achar BN, Narahari, Lorenzo CF, Hartley T (2005) Initialization Issues of the Caputo Fractional Derivative, Proceedings of IDETC/CIE 2005, Sept. 24-28, Long Beach CA. DETC2005. pp. 1-8.
13. Mainardi F, Gorenflo R (2000) On Mittag-Leffler-type functions in fractional evolution processes. J. Comp. Appl. Math. 118:283-299.