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2011 | 9 | 5 | 1267-1279
Tytuł artykułu

Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a study of fractional configurations in gravity theories and Lagrange mechanics. The approach is based on a Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists of a proof that, for corresponding classes of nonholonomic distributions, a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.
Wydawca

Czasopismo
Rocznik
Tom
9
Numer
5
Strony
1267-1279
Opis fizyczny
Daty
wydano
2011-10-01
online
2011-09-15
Twórcy
  • Department of Mathematics and Computer Sciences, Çankaya University, 06530, Ankara, Turkey, dumitru@cancaya.edu.tr
  • Science Department, University “Al. I. Cuza” Iaşi, 54, Lascar Catargi street, Iaşi, Romania, 700107, sergiu.vacaru@uaic.ro
Bibliografia
  • [1] S. Anco, J. Phys. A: Math. Gen. 39, 2043 (2006) http://dx.doi.org/10.1088/0305-4470/39/9/005[Crossref]
  • [2] S. Anco, S. Vacaru, J. Geom. Phys. 59, 79 (2009) http://dx.doi.org/10.1016/j.geomphys.2008.10.006[Crossref]
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  • [4] D. Baleanu, S. Vacaru, Nonlin. Dyn. 64, 365 (2011) http://dx.doi.org/10.1007/s11071-010-9867-3[Crossref]
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  • [6] D. Baleanu, S. Vacaru, arXiv:1007.2866v3 [math-ph]
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  • [18] S. Vacaru, Int. J. Geom. Meth. Mod. Phys. 5, 473 (2008) http://dx.doi.org/10.1142/S0219887808002898[Crossref]
  • [19] S. Vacaru, Acta Appl. Math. 110, 73 (2010) http://dx.doi.org/10.1007/s10440-008-9387-z[Crossref]
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  • [22] A.A. Kilbas, H. H. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, (Elsevier, Amsterdam, 2006)
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
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