Browsing by Author "Vacaru, Sergiu I."

Now showing 1 - 4 of 4

Citation - WoS: 20
Citation - Scopus: 24
Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics
(versita, 2011) Vacaru, Sergiu I.; Baleanu, Dumitru
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.
Citation - WoS: 18
Citation - Scopus: 22
Fedosov Quantization of Fractional Lagrange Spaces
(Springer/plenum Publishers, 2011) Vacaru, Sergiu I.; Baleanu, Dumitru
The main goal of this work is to perform a nonholonomic deformation (Fedosov type) quantization of fractional Lagrange-Finsler geometries. The constructions are provided for a fractional almost Kahler model encoding equivalently all data for fractional Euler-Lagrange equations with Caputo fractional derivative.
Citation - WoS: 23
Citation - Scopus: 25
Fractional Almost Kahler-Lagrange Geometry
(Springer, 2011) Vacaru, Sergiu I.; Baleanu, Dumitru
The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kahler geometry. We use the fractional Caputo derivative generalized for nontrivial nonlinear connections (N-connections) originally introduced in Finsler geometry, with further developments in Lagrange and Hamilton geometry. For fundamental geometric objects induced canonically by regular Lagrange functions, we construct compatible almost symplectic forms and linear connections completely determined by a "prime" Lagrange (in particular, Finsler) generating function. We emphasize the importance of such constructions for deformation quantization of fractional Lagrange geometries and applications in modern physics.
Citation - WoS: 15
Citation - Scopus: 18
Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics
(Amer inst Physics, 2011) Vacaru, Sergiu I.; Baleanu, Dumitru
Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric data for such models are encoded into (fractional) bi-Hamiltonian structures and associated solitonic hierarchies. The constructions yield horizontal/vertical pairs of fractional vector sine-Gordon equations and fractional vector mKdV equations when the hierarchies for corresponding curve fractional flows are described in explicit forms by fractional wave maps and analogs of Schrodinger maps. (C) 2011 American Institute of Physics. [doi:10.1063/1.3589964]