Fractional Dynamical Systems on Fractional Leibniz Algebroids

TL;DR

This paper introduces fractional tangent bundles and Leibniz algebroids, exploring their geometric properties and analyzing fractional dynamical systems within this framework, with applications across physics, mechanics, and economics.

Contribution

It defines fractional tangent bundles and Leibniz algebroids using Miron's method, extending geometric structures to fractional calculus.

Findings

Development of fractional tangent bundle concept

Investigation of fractional Leibniz algebroids

Discussion of fractional dynamical systems on these structures

Abstract

The theory of derivative of noninteger order goes back to Leibniz, Liouville and Riemann. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics. In this paper we define the fractional tangent bundle on a manifold, using a method of Radu Miron. The fractional Leibniz algebroids are investigated. The associated objects have an geometric character. Some fractional dynamical systems on a fractional Leibniz algebroid are disscussed.