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2013 | 11 | 10 | 1295-1303
Tytuł artykułu

Fractional nonlinear systems with sequential operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper possible approximation of solutions to initial value problems stated for fractional nonlinear equations with sequential derivatives of Caputo type is presented. We proved that values of Caputo derivatives in continuous case can be approximated by corresponding values of h-difference operators with h being small enough. Numerical examples are presented.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1295-1303
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-12-19
Twórcy
  • Bialystok University of Technology, ul. Wiejska 45a, 15-351, Białystok, Poland, d.mozyrska@pb.edu.pl
autor
  • Bialystok University of Technology, ul. Wiejska 45a, 15-351, Białystok, Poland, e.girejko@pb.edu.pl
  • Bialystok University of Technology, ul. Wiejska 45a, 15-351, Białystok, Poland, m.wyrwas@pb.edu.pl
Bibliografia
  • [1] J. A. T. Machado, Syst. Anal. Model. Sim. 27, 107 (1997)
  • [2] D. Baleanu, H. Mohammadi, Sh. Rezapour, Abstr. Appl. Anal. 2012, 837437 (2012)
  • [3] A. Debbouche, D. Baleanu, R. P. Agarwal, Bound. Value Prob. 2012, 78 (2012) http://dx.doi.org/10.1186/1687-2770-2012-78[Crossref]
  • [4] G. Wang, D. Baleanu, L. Zhang, Fractional Calculus & Applied Analysis 15, 244 (2012) http://dx.doi.org/10.2478/s13540-012-0018-z[Crossref]
  • [5] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation (John Wiley & Sons, 1993)
  • [6] I. Podlubny, Fractional Differential Equations (Academic Press, New York, NY, 1999)
  • [7] A. D. Polyanin, V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations (Chapman & Hall, CRC, Boca Raton, 2004)
  • [8] B. Ahmad, J. J. Nieto, Comput. Math. Appl. 64, 3046 (2012) http://dx.doi.org/10.1016/j.camwa.2012.02.036[Crossref]
  • [9] C. Bai, J. Math. Anal. Appl. 384, 211 (2011) http://dx.doi.org/10.1016/j.jmaa.2011.05.082[Crossref]
  • [10] D. Baleanu, O. G. Mustafa, R. P. Agarwal, J. Phys. A-Math. Theor. 43, 385209 (2010) http://dx.doi.org/10.1088/1751-8113/43/38/385209[Crossref]
  • [11] A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem (Oxford University Press, 2000)
  • [12] F. T. Akyildiz, H. Bellout, K. Vajravelu, R. A. Van Gorder, Nonlinear Anal.-Real 12, 2919 (2011) http://dx.doi.org/10.1016/j.nonrwa.2011.02.017[Crossref]
  • [13] B. Ahmad, J. J. Nieto, A. Alsaedi, M. El-Shahed, Nonlinear Anal.-Real 13, 599 (2012) http://dx.doi.org/10.1016/j.nonrwa.2011.07.052[Crossref]
  • [14] K. S. Miller, B. Ross, In: International Symposium on Univalent Functions, Fractional Calculus and their Applications, Nihon University, Kōriyama, Japan 139 (1988)
  • [15] M. Klimek, Commun. Nonlinear Sci. 16, 4689 (2011) http://dx.doi.org/10.1016/j.cnsns.2011.01.018[Crossref]
  • [16] K. M. Furati, Bound. Value Prob. 2012, 58 (2012) http://dx.doi.org/10.1186/1687-2770-2012-58[Crossref]
  • [17] K. Diethelm, N. J. Ford, A. D. Freed, Y. Luchko, Comput. Method Appl. M. 194, 743 (2005) http://dx.doi.org/10.1016/j.cma.2004.06.006[Crossref]
  • [18] G. B. Loghmani, S. Javanmardi, B. Malays. Math. Sci. Soc. 35, 315 (2012)
  • [19] Z. S. I. Mansour, Fractional Calculus & Applied Analysis 12, 159 (2009)
  • [20] D. Mozyrska, E. Girejko, In: A. Almeida, L. Castro, F. O. Speck (Ed.), Advances in Harmonic Analysis and Operator Theory - The Stefan Samko Anniversary Volume, Operator Theory: Advances and Applications, 388 (Birkhäuser, 2013)
  • [21] E. Girejko, D. Mozyrska, M. Wyrwas, Fractional Discrete Systems with Sequential h-differences, arXiv:1304.3484
  • [22] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations (Elsevier, 2006)
  • [23] R. A. C. Ferreira, D. F. M. Torres, Applicable Analysis and Discrete Mathematics 5, 110 (2011) http://dx.doi.org/10.2298/AADM110131002F[Crossref]
  • [24] N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres, Discrete Cont. Dyn. S. 29, 417 (2011) http://dx.doi.org/10.3934/dcds.2011.29.417[Crossref]
  • [25] M. T. Holm, Ph.D. thesis, University of Nebraska (Lincoln, USA, 2011)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0223-3
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