Fractional driven-damped oscillator and its general closed form exact solution
New questions in fundamental physics and in other fields, which cannot be formulated adequately using traditional integral and differential calculus emerged recently. Fractional calculus was shown to describe phenomena where conventional approaches have been unsatisfactory. The driven damped fractio...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
9 April 2018
|
| In: |
Physica. A, Statistical mechanics and its applications
Year: 2018, Volume: 505, Pages: 744-762 |
| ISSN: | 1873-2119 |
| DOI: | 10.1016/j.physa.2018.03.044 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1016/j.physa.2018.03.044 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0378437118303649 
|
| Author Notes: | Michael Berman, Lorenz S. Cederbaum |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1669468313 | ||
| 003 | DE-627 | ||
| 005 | 20230427111703.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 190719s2018 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1016/j.physa.2018.03.044 |2 doi | |
| 035 | |a (DE-627)1669468313 | ||
| 035 | |a (DE-599)KXP1669468313 | ||
| 035 | |a (OCoLC)1341233809 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 29 |2 sdnb | ||
| 100 | 1 | |a Berman, Michael |e VerfasserIn |0 (DE-588)1190850656 |0 (DE-627)1669448924 |4 aut | |
| 245 | 1 | 0 | |a Fractional driven-damped oscillator and its general closed form exact solution |c Michael Berman, Lorenz S. Cederbaum |
| 264 | 1 | |c 9 April 2018 | |
| 300 | |a 19 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 19.07.2019 | ||
| 520 | |a New questions in fundamental physics and in other fields, which cannot be formulated adequately using traditional integral and differential calculus emerged recently. Fractional calculus was shown to describe phenomena where conventional approaches have been unsatisfactory. The driven damped fractional oscillator entails a rich set of important features, including loss of energy to the environment and resonances. In this paper, this oscillator with Caputo fractional derivatives is solved analytically in closed form. The exact solution is expressed in terms of generalized Mittag-Leffler functions. The standard driven-damped Harmonic Oscillator is recovered as a special case of non-fractional derivatives. In contradistinction to the standard oscillator, the solution of the fractional oscillator is shown to decay algebraically and to possess a finite number of zeros. Several decay patterns are uncovered and are a direct consequence of the asymptotic properties of the generalized Mittag-Leffler functions. Other interesting properties of the fractional oscillator like the momentum–position phase-plane diagrams and the time dependence of the energy terms are discussed as well. | ||
| 650 | 4 | |a derivatives | |
| 650 | 4 | |a Driven damped Harmonic Oscillator | |
| 650 | 4 | |a Driven damped oscillator | |
| 650 | 4 | |a Exact closed-form solution | |
| 650 | 4 | |a Fractional calculus | |
| 650 | 4 | |a functions | |
| 650 | 4 | |a Laplace transforms | |
| 700 | 1 | |a Cederbaum, Lorenz S. |d 1946- |e VerfasserIn |0 (DE-588)172484952 |0 (DE-627)697422798 |0 (DE-576)133346145 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Physica. A, Statistical mechanics and its applications |d Amsterdam : North Holland Publ. Co., 1975 |g 505(2018), Seite 744-762 |h Online-Ressource |w (DE-627)266015077 |w (DE-600)1466577-3 |w (DE-576)074959832 |x 1873-2119 |7 nnas |a Fractional driven-damped oscillator and its general closed form exact solution |
| 773 | 1 | 8 | |g volume:505 |g year:2018 |g pages:744-762 |g extent:19 |a Fractional driven-damped oscillator and its general closed form exact solution |
| 856 | 4 | 0 | |u https://doi.org/10.1016/j.physa.2018.03.044 |x Verlag |x Resolving-System |3 Volltext |
| 856 | 4 | 0 | |u http://www.sciencedirect.com/science/article/pii/S0378437118303649 |x Verlag |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20190719 | ||
| 993 | |a Article | ||
| 994 | |a 2018 | ||
| 998 | |g 172484952 |a Cederbaum, Lorenz S. |m 172484952:Cederbaum, Lorenz S. |d 120000 |d 120300 |d 120000 |e 120000PC172484952 |e 120300PC172484952 |e 120000PC172484952 |k 0/120000/ |k 1/120000/120300/ |k 0/120000/ |p 2 |y j | ||
| 999 | |a KXP-PPN1669468313 |e 349504552X | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"name":{"displayForm":["Michael Berman, Lorenz S. Cederbaum"]},"recId":"1669468313","id":{"eki":["1669468313"],"doi":["10.1016/j.physa.2018.03.044"]},"title":[{"title":"Fractional driven-damped oscillator and its general closed form exact solution","title_sort":"Fractional driven-damped oscillator and its general closed form exact solution"}],"person":[{"given":"Michael","roleDisplay":"VerfasserIn","display":"Berman, Michael","family":"Berman","role":"aut"},{"roleDisplay":"VerfasserIn","given":"Lorenz S.","display":"Cederbaum, Lorenz S.","family":"Cederbaum","role":"aut"}],"type":{"bibl":"article-journal","media":"Online-Ressource"},"origin":[{"dateIssuedKey":"2018","dateIssuedDisp":"9 April 2018"}],"language":["eng"],"relHost":[{"corporate":[{"role":"isb","display":"Hollandsche Maatschappij der Wetenschappen","roleDisplay":"Herausgebendes Organ"}],"origin":[{"publisherPlace":"Amsterdam","dateIssuedDisp":"1975-","publisher":"North Holland Publ. Co.","dateIssuedKey":"1975"}],"language":["eng"],"disp":"Fractional driven-damped oscillator and its general closed form exact solutionPhysica. A, Statistical mechanics and its applications","physDesc":[{"extent":"Online-Ressource"}],"note":["Gesehen am 11.04.23"],"name":{"displayForm":["Hollandsche Maatschappij der Wetenschappen, Haarlem"]},"pubHistory":["Nachgewiesen 79.1975 - 392.2013; Vol. 393.2014 -"],"id":{"zdb":["1466577-3"],"eki":["266015077"],"issn":["1873-2119"]},"recId":"266015077","titleAlt":[{"title":"Physica / A"},{"title":"Statistical and theoretical physics"},{"title":"Statistical mechanics and its applications"}],"title":[{"title":"Physica","partname":"Statistical mechanics and its applications","subtitle":"europhysics journal","title_sort":"Physica"}],"type":{"bibl":"periodical","media":"Online-Ressource"},"part":{"pages":"744-762","year":"2018","text":"505(2018), Seite 744-762","extent":"19","volume":"505"}}],"physDesc":[{"extent":"19 S."}],"note":["Gesehen am 19.07.2019"]} | ||
| SRT | |a BERMANMICHFRACTIONAL9201 | ||