# 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.

## Key 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.

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Source: https://tomesphere.com/paper/0704.0519