Fractional Hamiltonian analysis of higher order derivatives systems

2006/10/01 by Dumitru Baleanu, Dumitru Bǎleanu, Sami I. Muslih +2
Mathematics · Physics and Astronomy · #Anharmonicity #Black Holes and Theoretical Physics #Fractional Differential Equations Solutions #Fractional calculus #Hamiltonian (control theory) #Hamiltonian system #Harmonic oscillator #Integer (computer science) #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Order (exchange) #Path integral formulation #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #math-ph #math.MP

paper · pdf · doi:10.1063/1.2356797

published as Journal of Mathematical Physics 47 (10): Art. No. 103503, (2006) · 13 pages

openalex publication_date 2006/10/01 · arxiv created 2006/12/07 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Physical degrees of freedom of non-local theories
• Lagrangian Formulation of Classical Fields within Riemann-Liouville Fractional Derivatives
• Time fractional Schrödinger equation
• Higher-derivative Lagrangians, nonlocality, problems, and solutions
• Fractional Differential Equations