Fractional Almost Kahler - Lagrange Geometry
Abstract
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 and, in our approach, with fractional derivatives. 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.
Cite
@article{arxiv.1006.5535,
title = {Fractional Almost Kahler - Lagrange Geometry},
author = {Dumitru Baleanu and Sergiu I. Vacaru},
journal= {arXiv preprint arXiv:1006.5535},
year = {2011}
}
Comments
latex2e, 17 pages, v3 performed following requests of referee with additional references and explanations; accepted to "Nonlinear Dynamics"