Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics
arXiv:1007.2864 · doi:10.2478/s11534-011-0040-5
Abstract
We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on 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 in 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.
latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated references
References in corpus (6)
- Fractional Calculus: Integral and Differential Equations of Fractional Order
- Fractional Vector Calculus and Fractional Maxwell's Equations
- Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
- Fractional Nonholonomic Ricci Flows
- Fractional Almost Kahler - Lagrange Geometry
- Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons