Preferences help
enabled [disable] Abstract
Number of results
2013 | 11 | 10 | 1433-1439
Article title

Numerical approach to the Caputo derivative of the unknown function

Title variants
Languages of publication
If a function can be explicitly expressed, then one can easily compute its Caputo derivative by the known methods. If a function cannot be explicitly expressed but it satisfies a differential equation, how to seek Caputo derivative of such a function has not yet been investigated. In this paper, we propose a numerical algorithm for computing the Caputo derivative of a function defined by a classical (integer-order) differential equation. By the properties of Caputo derivative derived in this paper, we can change the original typical differential system into an equivalent Caputo-type differential system. Numerical examples are given to support the derived numerical method.
Physical description
1 - 10 - 2013
19 - 12 - 2013
  • [1] K. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993)
  • [2] K. B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, New York, 1974)
  • [3] S. G. Samko, A. A. Kilbas, O. I. and Marichev, Fractional Integrals and Derivatives (Gordon and breach Science, Yverdon, Switzerland, 1993)
  • [4] I. Podlubny, Fractional Differential Equations (Acdemic Press, San Dieg, 1999)
  • [5] C. P. Li, Y. J. Wu, R. S. Ye eds., Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis: Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Numerical Simulations (World Scientific, 2013)
  • [6] R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)[Crossref]
  • [7] I. Podlubny, A. Chechkin, T. Skovranek, Y. Q. Chen, B. Vinagre, J. Comput. Phys. 228, 3137 (2009)[Crossref]
  • [8] A. Schmidt, L. Gaul, Signal Process. 86, 2592 (2006).[Crossref]
  • [9] C. P. Li, F. H. Zeng, Numer. Funct. Anal. Optimiz. 34, 149 (2013)[Crossref]
  • [10] K. Diethelm, N. J. Ford, A. D, Freed, Y. Luchko, Comput. Methods Appl. Mech. Engrg. 194, 743 (2005)[Crossref]
  • [11] C. Lubich, SIAM J. Math. Anal. 17, 704 (1986)[Crossref]
  • [12] V. E. Lynch, B. A. Carreras, D. del-Castillo-Negrete, K. M. Ferreira-Mejias, H.R. Hicks, J. Comput. Phys. 192, 406 (2003)[Crossref]
  • [13] C.P. Li, A. Chen, J.J. Ye, J. Comput. Phys. 230, 3352 (2011)[Crossref]
  • [14] Z. M. Odibat, Math. Comput. Simulat. 79, 2013 (2009)[Crossref]
  • [15] C. P. Li, F.H. Zeng, Int. J. Bifurcat. Chaos 22, 1230014 (2012)[Crossref]
  • [16] E. Sousa, Int. J. Bifurcat. Chaos 22, 1250075 (2012)[Crossref]
  • [17] C. P. Li, D. L. Qian, Y. Q. Chen, Disctete Dyn. Nat. Soc. 2011, 562494 (2011)
  • [18] C. P. Li, W. H. Deng, Appl. Math. Comput. 187, 777 (2007)[Crossref]
  • [19] C.P. Li, Z. Zhao, Euro. Phys. J.-Spec. Top. 193, 5 (2011)[Crossref]
  • [20] K. Diethelm, N. J. Ford, A. D. Freed, Numer. Algorithms 36, 31 (2004)[Crossref]
  • [21] C. Yang, F. Liu, ANZIAM J. 47, 168 (2006)
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.