Hamilton-Jacobi Fractional Sequential Mechanics

TL;DR

This paper extends Hamilton-Jacobi mechanics to fractional derivatives, providing a generalized formalism applicable to fractional systems and demonstrating its consistency with existing approaches through example problems.

Contribution

It introduces a fractional Hamilton-Jacobi formalism applicable to systems with fractional derivatives, aligning with prior fractional mechanics frameworks.

Findings

Exact agreement with Agrawal's formalism

Formalism applicable to fractional derivative systems

Demonstrated through example problems

Abstract

As a continuation of Rabei et al. work [11], the Hamilton- Jacobi partial differential equation is generalized to be applicable for systems containing fractional derivatives. The Hamilton- Jacobi function in configuration space is obtained in a similar manner to the usual mechanics. Two problems are considered to demonstrate the application of the formalism. The result found to be in exact agreement with Agrawal's formalism.