Fractional Almost Kahler - Lagrange Geometry

Details Fractional Almost Kahler - Lagrange Geometry Fractional Almost Kahler - Lagrange Geometry

2010-06-29

arxiv.org/abs/1006.5535v3

Nonlinear Dyn.64:365-373,2011

Physics

Mathematical Physics

latex2e, 17 pages, v3 performed following requests of referee with additional references and explanations; accepted to "Nonlin

Scientific paper

10.1007/s11071-010-9867-3

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.

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