Fractional Analogous Models in Mechanics and Gravity Theories

TL;DR

This paper reviews recent advances in the geometry of nonholonomic manifolds, fractional calculus, and their application to developing models of fractional gravity and mechanics.

Contribution

It introduces fractional models of gravity and mechanics based on nonholonomic geometry and Caputo derivatives, expanding classical theories with fractional calculus.

Findings

Development of fractional gravity models

Application of Caputo derivatives in mechanics

Extension of Lagrange--Finsler geometry to fractional calculus

Abstract

We briefly review our recent results on the geometry of nonholonomic manifolds and Lagrange--Finsler spaces and fractional calculus with Caputo derivatives. Such constructions are used for elaborating analogous models of fractional gravity and fractional Lagrange mechanics.