Fractional Complex Euler–Lagrange Equation: Nonconservative Systems
Classical forbidden processes paved the way for the description of mechanical systems with the help of complex Hamiltonians. Fractional integrals of complex order appear as a natural generalization of those of real order. We propose the complex fractional Euler-Lagrange equation, obtained by finding...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/11/799 |
| _version_ | 1797459236369727488 |
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| author | Antonela Toma Octavian Postavaru |
| author_facet | Antonela Toma Octavian Postavaru |
| author_sort | Antonela Toma |
| collection | DOAJ |
| description | Classical forbidden processes paved the way for the description of mechanical systems with the help of complex Hamiltonians. Fractional integrals of complex order appear as a natural generalization of those of real order. We propose the complex fractional Euler-Lagrange equation, obtained by finding the stationary values associated with the fractional integral of complex order. The complex Hamiltonian obtained from the Lagrangian is suitable for describing nonconservative systems. We conclude by presenting the conserved quantities attached to Noether symmetries corresponding to complex systems. We illustrate the theory with the aid of the damped oscillatory system. |
| first_indexed | 2024-03-09T16:48:33Z |
| format | Article |
| id | doaj.art-12d249da7b62432ca647ff5580b5e560 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T16:48:33Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-12d249da7b62432ca647ff5580b5e5602023-11-24T14:43:01ZengMDPI AGFractal and Fractional2504-31102023-11-0171179910.3390/fractalfract7110799Fractional Complex Euler–Lagrange Equation: Nonconservative SystemsAntonela Toma0Octavian Postavaru1Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, RomaniaCenter for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, RomaniaClassical forbidden processes paved the way for the description of mechanical systems with the help of complex Hamiltonians. Fractional integrals of complex order appear as a natural generalization of those of real order. We propose the complex fractional Euler-Lagrange equation, obtained by finding the stationary values associated with the fractional integral of complex order. The complex Hamiltonian obtained from the Lagrangian is suitable for describing nonconservative systems. We conclude by presenting the conserved quantities attached to Noether symmetries corresponding to complex systems. We illustrate the theory with the aid of the damped oscillatory system.https://www.mdpi.com/2504-3110/7/11/799complex fractional integralcomplex Hamiltonian dynamicsymmetries |
| spellingShingle | Antonela Toma Octavian Postavaru Fractional Complex Euler–Lagrange Equation: Nonconservative Systems Fractal and Fractional complex fractional integral complex Hamiltonian dynamic symmetries |
| title | Fractional Complex Euler–Lagrange Equation: Nonconservative Systems |
| title_full | Fractional Complex Euler–Lagrange Equation: Nonconservative Systems |
| title_fullStr | Fractional Complex Euler–Lagrange Equation: Nonconservative Systems |
| title_full_unstemmed | Fractional Complex Euler–Lagrange Equation: Nonconservative Systems |
| title_short | Fractional Complex Euler–Lagrange Equation: Nonconservative Systems |
| title_sort | fractional complex euler lagrange equation nonconservative systems |
| topic | complex fractional integral complex Hamiltonian dynamic symmetries |
| url | https://www.mdpi.com/2504-3110/7/11/799 |
| work_keys_str_mv | AT antonelatoma fractionalcomplexeulerlagrangeequationnonconservativesystems AT octavianpostavaru fractionalcomplexeulerlagrangeequationnonconservativesystems |