Fractional Hamiltonian analysis of higher order derivatives systems

TL;DR

This paper develops a fractional Hamiltonian framework for higher-order derivative systems, applying it to field theory and oscillators, and recovers classical results when fractional derivatives are replaced by integer derivatives.

Contribution

It introduces a fractional Ostrogradski's formulation for higher-order systems and analyzes fractional path integrals for oscillators, extending classical mechanics to fractional calculus.

Findings

Fractional Hamiltonian analysis of 1+1D field theory.

Fractional path integral formulations for oscillators.

Recovery of classical results with integer derivatives.

Abstract

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.