Fractional dynamical systems and applications in mechanics and economics

TL;DR

This paper develops a geometric framework using fractional calculus on manifolds, deriving fractional Euler-Lagrange equations and illustrating their applications in mechanics and economics.

Contribution

It introduces a fractional jet fibre bundle structure and formulates fractional Euler-Lagrange equations, expanding the geometric tools for mechanics and economics modeling.

Findings

Fractional calculus applied to geometric structures on manifolds.

Derivation of fractional Euler-Lagrange equations.

Applications demonstrated in mechanics and economics contexts.

Abstract

Using the fractional integration and differentiation on R we build the fractional jet fibre bundle on a differentiable manifold and we emphasize some important geometrical objects. Euler-Lagrange fractional equations are described. Some significant examples from mechanics and economics are presented.