PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2013 | 11 | 10 | 1295-1303
Article title

Fractional nonlinear systems with sequential operators

Content
Title variants
Languages of publication
EN
Abstracts
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.
Publisher

Journal
Year
Volume
11
Issue
10
Pages
1295-1303
Physical description
Dates
published
1 - 10 - 2013
online
19 - 12 - 2013
Contributors
  • Bialystok University of Technology, ul. Wiejska 45a, 15-351, Białystok, Poland, d.mozyrska@pb.edu.pl
author
  • 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
References
  • [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)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0223-3
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.