Hamilton-Jacobi formulation of systems within Caputo's fractional derivative

TL;DR

This paper develops a fractional Hamilton-Jacobi framework for discrete systems using Caputo derivatives, deriving the fractional action and solving the equations of motion with an illustrative example.

Contribution

It introduces a novel fractional Hamilton-Jacobi formulation for discrete systems based on Caputo derivatives, expanding classical mechanics into fractional calculus.

Findings

Derived the fractional action function for discrete systems.

Solved equations of motion within the fractional framework.

Provided a detailed example illustrating the method.

Abstract

In this paper we develop a fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives. The fractional action function is obtained and the solutions of the equations of motion are recovered. An example is studied in details.