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Tytuł artykułu

Cone solutions of multi-order fractional difference systems

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The fractional difference system of equations with different fractional orders is considered. We obtain the existence and uniqueness results for the initial value problem. Cone solutions are presented. An example is given to illustrate the results.
Rocznik
Strony
419--429
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
  • Faculty of Computer Science Bialystok University of Technology Wiejska 45A, 15-351 Białystok, Poland
autor
  • Faculty of Computer Science Bialystok University of Technology Wiejska 45A, 15-351 Białystok, Poland
Bibliografia
  • 1. Abdeljawad, T. (2011) On Riemann and Caputo fractional differences. Comp. and Math. with Appl., doi: 10.1016/j.camwra.2011.03.036
  • 2. Atici, F. M. and Eloe, P. W. (2007) A transform method in discrete fractional calculus. International Journal of Difference Equations, 2(2):165–176.
  • 3. Atici, F. M. and Eloe, P. W. (2008) Initial value problems in discrete fractiona calculus. Proceedings of the American Mathematical Society, S 0002-9939(08)09626-3:9.
  • 4. Chen, F., Luo, X. and Zhou, Y. (2011) Existence results for nonlinear fractional difference equation. Advances in Difference Equations, 2011:12 pages, doi: 10.1155/2011/713201.
  • 5. Dzielinski, A. and Sierociuk, D. (2008) Stability of discrete fractional order statespace systems. Journal of Vibration and Control, 14(9-10):1543–1556.
  • 6. Goodrich, Ch. S. (2012) On discrete sequential fractional boundary value problems. Journal of Mathematical Analysis and Applications, 385(1):111–124.
  • 7. Holm, M. T. (2011) The theory of discrete fractional calculus: Development and application. University of Nebraska - Lincoln.
  • 8. Kaczorek, T. (2006) Computation of realizations of discrete-time cone systems. Bulletin of the Polish Academy of Sciences, 54(3):347–350.
  • 9. Kaczorek, T. (2007) Reachability and controllability to zero of positive fractional discrete-time systems. Machine Intelligence and Robotic Control, 6(4).
  • 10. Kaczorek, T. (2008) Fractional positive continuous time linear systems and their reachability. Int. J. Appl. Math. Comput. Sci., 18(2):223–228.
  • 11. Kaczorek, T. (2009) Reachability of cone fractional continuous-time linear systems. Int. J. Appl. Math. Comput. Sci., 19(1):89–93.
  • 12. Kaczorek, T. (2011) Selected Problems of Fractional Systems Theory, LNCIS 411, Springer.
  • 13. Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J. (2006) Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B. V., Amsterdam.
  • 14. Miller, K. S. and Ross, B. (1988) Fractional difference calculus. Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and their Applications, Nihon University, Kōriyama, Japan, 139–152.
  • 15. Mozyrska, D. and Girejko, E. (2013) Overview of the fractional difference operators appearing in linear systems theory. In: Advances in Harmonic Analysis and Operator Theory - The Stefan Samko Anniversary Volume, Operator Theory: Advances and Applications. Birkhäuser, 253–267.
  • 16. Mozyrska, D., Girejko, E. and Wyrwas, M. (2012) Nonlinear fractional cone systems with the Caputo derivative. Applied Mathematics Letters, 25:752–756.
  • 17. Ostalczyk, P. (2012) Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains. International Journal of Applied Mathematics and Computer Science, 22(3):533–538.
  • 18. Podlubny, I. (1999) Fractional Differential Equations. Mathematics in Sciences and Engineering 198. Academic Press, San Diego.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c529eb0f-745a-4e19-8be9-1875fcbac307
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