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2013 | 11 | 10 | 1262-1267
Tytuł artykułu

A discrete time method to the first variation of fractional order variational functionals

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Grünwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1262-1267
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-12-19
Twórcy
  • Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal, spooseh@ua.pt
  • Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal, ricardo.almeida@ua.pt
  • Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal, delfim@ua.pt
Bibliografia
  • [1] A. B. Malinowska, D.F.M. Torres, Introduction to the fractional calculus of variations (Imp. Coll. Press, London, 2012)
  • [2] O. P. Agrawal, O. Defterli, D. Baleanu, J. Vib. Control 16, 1967 (2010) http://dx.doi.org/10.1177/1077546309353361[Crossref]
  • [3] O. P. Agrawal, S.I. Muslih, D. Baleanu, Commun. Nonlinear Sci. Numer. Simul. 16, 4756 (2011) http://dx.doi.org/10.1016/j.cnsns.2011.05.002[Crossref]
  • [4] R. Almeida, D.F.M. Torres, Appl. Math. Comput. 217, 956 (2010) http://dx.doi.org/10.1016/j.amc.2010.03.085[Crossref]
  • [5] D. Baleanu, O. Defterli, O.P. Agrawal, J. Vib. Control 15, 583 (2009) http://dx.doi.org/10.1177/1077546308088565[Crossref]
  • [6] D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional calculus, Models and numerical methods (World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012)
  • [7] S. Pooseh, R. Almeida, D.F.M. Torres, Comput. Math. Appl. 64, 3090 (2012) http://dx.doi.org/10.1016/j.camwa.2012.01.068[Crossref]
  • [8] A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies 204 (Elsevier, Amsterdam, 2006)
  • [9] I. Podlubny, Fractional differential equations (Academic Press, San Diego, CA, 1999)
  • [10] F. Riewe, Phys. Rev. E 55, 3581 (1997) http://dx.doi.org/10.1103/PhysRevE.55.3581[Crossref]
  • [11] O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002) http://dx.doi.org/10.1016/S0022-247X(02)00180-4[Crossref]
  • [12] J. Gregory, C. Lin, SIAM J. Numer. Anal. 30, 871 (1993) http://dx.doi.org/10.1137/0730045[Crossref]
  • [13] J. Gregory, R.S. Wang, SIAM J. Numer. Anal. 27, 470 (1990) http://dx.doi.org/10.1137/0727029[Crossref]
  • [14] R. Almeida, R.A.C. Ferreira, D.F.M. Torres, Acta Math. Sci. Ser. B Engl. Ed. 32, 619 (2012)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0250-0
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