Fractional Exact Solutions and Solitons in Gravity

TL;DR

This paper reviews recent developments in fractional gravity theory, demonstrating how geometric data can be encoded into solitonic hierarchies using Caputo derivatives and nonlinear connections.

Contribution

It introduces a main theorem linking geometric data in gravity to solitonic hierarchies within the fractional calculus framework.

Findings

Encoding of geometric data into solitonic hierarchies

Application of Caputo fractional derivatives in gravity

New formalism for fractional gravity theory

Abstract

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.