期刊
NONLINEAR DYNAMICS
卷 64, 期 4, 页码 365-373出版社
SPRINGER
DOI: 10.1007/s11071-010-9867-3
关键词
Fractional derivatives and integrals; Fractional Lagrange mechanics; Nonlinear connections; Almost Kahler geometry
资金
- Cankaya University
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.
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