论文信息 - On the stable numerical evaluation of caputo fractional derivatives

On the stable numerical evaluation of caputo fractional derivatives

The computation of Caputo's fractional derivatives in the presence of measured data is considered as an ill-posed problem and treated by mollification techniques. It is shown that, with the appropriate choice of the radius of mollification, the method is a regularizing algorithm, and the order of convergence is derived. Error estimates are included together with numerical examples of interest.

Diego A. Murio | D. Murio

[1] S. Zhan,et al. Identification of parameters in one-dimensional IHCP , 1998 .

[2] I. Podlubny. Fractional differential equations , 1998 .

[3] F. Mainardi,et al. Fractals and fractional calculus in continuum mechanics , 1997 .

[4] Fawang Liu,et al. Numerical solution of the space fractional Fokker-Planck equation , 2004 .

[5] Diego Murio,et al. Mollification and space marching , 2002 .

[6] D. Murio,et al. Discrete mollification and automatic numerical differentiation , 1998 .

[7] Afonso Ferreira,et al. BOUNDING THE PROBABILITY OF SUCCESS OF STOCHASTIC METHODS FOR GLOBAL OPTIMIZATION , 1993 .

[8] Diego A. Murio,et al. The Mollification Method and the Numerical Solution of Ill-Posed Problems , 1993 .

[9] G. Wahba. Spline models for observational data , 1990 .

[10] Keith A. Woodbury,et al. Inverse Engineering Handbook , 2002 .

[11] Alan D. Freed,et al. On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity , 1999 .

[12] M. Meerschaert,et al. Finite difference approximations for fractional advection-dispersion flow equations , 2004 .