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2013 | 11 | 10 | 1433-1439
Tytuł artykułu

Numerical approach to the Caputo derivative of the unknown function

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1433-1439
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-12-19
Twórcy
autor
  • Department of Mathematics, Shanghai University, Shanghai, 200444, PR China
autor
  • Department of Mathematics, Shanghai University, Shanghai, 200444, PR China, lcp@shu.edu.cn
Bibliografia
  • [1] K. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993)
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  • [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)
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  • [10] K. Diethelm, N. J. Ford, A. D, Freed, Y. Luchko, Comput. Methods Appl. Mech. Engrg. 194, 743 (2005) http://dx.doi.org/10.1016/j.cma.2004.06.006[Crossref]
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  • [13] C.P. Li, A. Chen, J.J. Ye, J. Comput. Phys. 230, 3352 (2011) http://dx.doi.org/10.1016/j.jcp.2011.01.030[Crossref]
  • [14] Z. M. Odibat, Math. Comput. Simulat. 79, 2013 (2009) http://dx.doi.org/10.1016/j.matcom.2008.08.003[Crossref]
  • [15] C. P. Li, F.H. Zeng, Int. J. Bifurcat. Chaos 22, 1230014 (2012) http://dx.doi.org/10.1142/S0218127412300145[Crossref]
  • [16] E. Sousa, Int. J. Bifurcat. Chaos 22, 1250075 (2012) http://dx.doi.org/10.1142/S0218127412500757[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) http://dx.doi.org/10.1016/j.amc.2006.08.163[Crossref]
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  • [21] C. Yang, F. Liu, ANZIAM J. 47, 168 (2006)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0214-4
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