On the stable numerical evaluation of caputo fractional derivatives

Computers and Mathematics with Applications

Volumn 51, Issue 9-10, 2006, Pages 1539-1550

  Murio, D A ^a  

^a UNIVERSITY OF CINCINNATI   (United States)

Author keywords

Caputo derivatives; Ill posed problems; mollification; Numerical fractional differentiation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING;

CAPUTO DERIVATIVES; ILL-POSED PROBLEMS; MOLLIFICATION; NUMERICAL FRACTIONAL DIFFERENTIATION;

DATA REDUCTION;

EID: 33745699810     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2005.11.037     Document Type: Article

References (13)

1. Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer-Verlag, Berlin 291-348
2. Diethelm K., and Freed A.D. On the solution of nonlinear fractional order differential equations used in the modelling of viscoplasticity. Scientific Computing in Chemical Engineering II: Computational Fluid Dynamics, Reaction Engineering and Molecular Properties (1999), Springer-Verlag 217-224
3. Liu F., Anh V., and Turner I. Numerical solution of the space fractional Fokker-Planck equation. JCAM 166 (2004) 209-219
4. Meerschaert M.M., and Tadjeran C. Finite difference approximations for fractional advection-dispersion flow equations. JCAM 172 (2004) 65-77
5. Podlubny I. Fractional Differential Equations (1999), Academic Press, Heidelberg
6. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integrals and Derivatives (1993), Gordan and Breach Sciences Publishers
7. Oldman K.B., and Spanier J. The Fractional Calculus (1974)
8. Caputo M. Elastica e Dissipazione (1969), Zanichelli
9. Murio D.A., Mejfa C.E., and Zhan S. Discrete mollification and automatic numerical differentiation. Computers Math. Applic. 35 5 (1998) 1-16
10. Murio D.A. The Mollification Method and the Numerical Solution of Ill-Posed Problems (1993), John Wiley and Sons, Bologna
11. Chapter 14. Murio D.A. Mollification and Space Marching. In: Woodbury K. (Ed). Inverse Engineering Handbook (2002), CRC Press, New York
12. Mejfa C.E., and Murio D.A. Mollified hiperbolic method for coefficient identification problems. Computers Math. Applic. 25 5 (1993) 1-12
13. Wahba G. Spline models for observational data. BMS-NSF Regional Conference Series in Applied Mathematics (1996), SIAM, Boca Raton, FL