Fractional Exact Solutions and Solitons in Gravity
@article{Baleanu2010FractionalES, title={Fractional Exact Solutions and Solitons in Gravity}, author={Dumitru Baleanu and Sergiu I. Vacaru}, journal={arXiv: Mathematical Physics}, year={2010}, pages={229-236} }
We survay our recent results on fractional gravity theory. It is also provided the Main Theorem on encoding of geometric data (metrics and connections in gravity and geometric mechanics) into solitonic hierarchies. Our approach is based on Caputo fractional derivative and nonlinear connection formalism.
2 Citations
Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity
- Mathematics
- 2012
In this summary of Habilitation Thesis, it is outlined author's 18 years research activity on mathematical physics, geometric methods in particle physics and gravity, modifications and applications…
On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling
- Mathematics
- 2013
It has been pointed out that the derivative chains rules in fractional differential calculus via fractional calculus are not quite satisfactory as far as they can yield different results which depend…
References
SHOWING 1-8 OF 8 REFERENCES
Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics
- Mathematics
- 2011
Methods from the geometry of nonholonomic manifolds and Lagrange–Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and…
Fedosov Quantization of Fractional Lagrange Spaces
- Mathematics
- 2011
The main goal of this work is to perform a nonholonomic deformation (Fedosov type) quantization of fractional Lagrange–Finsler geometries. The constructions are provided for a fractional almost…
Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics
- Mathematics
- 2011
We present a study of fractional configurations in gravity theories and Lagrange mechanics. The approach is based on a Caputo fractional derivative which gives zero for actions on constants. We…
Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
- Mathematics
- 2012
We study the fractional gravity for spacetimes with non-integer fractional derivatives. Our constructions are based on a formalism with the fractional Caputo derivative and integral calculus adapted…
Fractional almost Kähler–Lagrange geometry
- Mathematics
- 2011
The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kähler geometry. We use the fractional Caputo derivative generalized for nontrivial…
Curve Flows and Solitonic Hierarchies Generated by Einstein Metrics
- Mathematics
- 2008
We investigate bi-Hamiltonian structures and mKdV hierarchies of solitonic equations generated by (semi) Riemannian metrics and curve flows of non-stretching curves. There are applied methods of the…