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.

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

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Cited by in corpus (7)

• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Fractional Nonholonomic Ricci Flows
• Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics
• Geometrical enhancement of the electric field: Application of fractional calculus in nanoplasmonics
• Fractional Analogous Models in Mechanics and Gravity Theories
• Geometry of fractional spaces
• Fractional Exact Solutions and Solitons in Gravity