Fractional dynamical systems defined on fractional jet bundle and applications in economics

TL;DR

This paper develops a geometric framework using Caputo fractional derivatives to define fractional jet bundles and explores fractional dynamical systems with applications in economics.

Contribution

It introduces a novel geometric approach to fractional dynamical systems on fractional jet bundles using Caputo derivatives, with economic applications.

Findings

Established fractional jet bundle structures using Caputo derivatives

Formulated fractional dynamical systems on these bundles

Applied the framework to economic models

Abstract

Using Caputo fractional derivative of order $\alpha $ we build the fractional jet bundle of order $\alpha $ and its main geometrical structures. Defined on that bundle, some fractional dynamical systems with applications to economics are studied.