Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

TL;DR

This paper develops fractional geometric models in gravity and mechanics using Caputo derivatives, demonstrating that many physical theories can be represented as nonholonomic manifolds with constant curvature, linking fractional dynamics to geometric structures.

Contribution

It introduces a method to model fractional physical interactions as nonholonomic manifolds with constant curvature, expanding geometric approaches in fractional gravity and mechanics.

Findings

Large class of physical theories modeled as nonholonomic manifolds with constant curvature

Fractional dynamics encoded into curve flows and solitonic hierarchies

Method of nonholonomic deformations for various fractional derivatives

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.