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Tytuł artykułu

Fractional derivative generalization of Noether’s theorem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples are presented as an application of the theory.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-05-25
zaakceptowano
2015-08-08
online
2015-12-23
Twórcy
  • Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
  • Department of Pure Mathematics,School of Mathematics, Iran University of Science
    and Technology, Narmak, Tehran, 1684613114, Iran
  • Department of Mathematical Sciences, University of South Africa, PO Box 392, UNISA 0003, South Africa and
    Department of Mathematics,University of Mazandaran, Babolsar, Iran
Bibliografia
  • [1] I. Podlubny, Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, SomeMethods of Their Solution and Some of Their Applications, (San Diego, CA: Academic), 1999.
  • [2] D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional calculus models and numerical methods, (Series on Complexity,Nonlinearity and Chaos), World Scientific, 2012.
  • [3] A.H. Bhrawy and M.A. Abdelkawy, J. Comput. Phys. 294, (2015), 462-483.
  • [4] H. Jafari, N. Kadkhoda, D. Baleanu , Nonlinear Dynamics, Vol. 81(3) 1569-1574, (2015).
  • [5] P.J. Olver, Applications of Lie groups to differential equations, Graduate Texts in Mathematics, vol. 107. Springer, New York, 1993.
  • [6] M. Nadjafikhah, V. Shirvani, J. Commun. Nonlinear Sci. Numer. Simul. 17, 14 pages (2012).
  • [7] A.R. Adem, B. Muatjetjeja, , Appl. Math. Lett. 48 109-117, (2015).[Crossref]
  • [8] R.K. Gazizov, A.A. Kasatkin, S.Yu. Lukashchuk, J. Phys. Scr. T136, 014016 (2009).
  • [9] E. Noether, Math-phys. Klasse, 24 pages (1918), which originally appeared in Transport Theory and Statistical Physics, 1 (3), 25pages (1971).
  • [10] M.A. Tavel, English translation of [9], http://arxiv.org/abs/physics/0503066v1.
  • [11] F. Riewe, Phys. Rev. E (3) 53 (2), 10 pages (1996).
  • [12] F. Riewe, Phys. Rev. E (3) 55 (3) (part B), 12 pages (1997).
  • [13] O.P. Agrawal, J. Math. Anal. Appl. 272 (1) 12 pages (2002).
  • [14] G.S.F. Frederico, D.F.M. Torres, J. Math. Anal. Appl. 334, 13 pages (2007).
  • [15] G.S.F. Frederico, D.F.M. Torres, J. Appl. Math. Comput. 217(3), 11 pages (2010).
  • [16] P.J. Torvik, R.L. Bagley, J.Applied Mechanics, Transactions of ASME, 51(2), 5 pages (1984).
  • [17] P.J. Torvik, R.L. Bagley, AIAA Journal, 21(5), 8 pages (1983).
  • [18] M. Caputo, J. R. Astr. Soc. 13, 11 pages (1967).
  • [19] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach,Yverdon, 1993.
  • [20] M. Nadjafikhah, F. Ahangari, J. Commu. Theor. Phys.(Beijing), 59(3), 4 pages (2013).
  • [21] E.A. Rawashdeh, J. Appl. Math. Comput. 174(2) , 8 pages (2006).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0086
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