Mathematical modeling of oscillator hereditarity
The paper considers hereditarity oscillator which is characterized by oscillation equation with derivatives of fractional order $\beta$ and $\gamma$, which are defined in terms of Gerasimova-Caputo. Using Laplace transform were obtained analytical solutions and the Greens function, which are determi...
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| Format: | Article |
| Language: | Russian |
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Institute of Computer Science
2015-10-01
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| Series: | Компьютерные исследования и моделирование |
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| Online Access: | http://crm.ics.org.ru/uploads/crmissues/crm_2015_5/15.07.03.pdf |
| _version_ | 1818269227693375488 |
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| author | Roman Ivanovich Parovik |
| author_facet | Roman Ivanovich Parovik |
| author_sort | Roman Ivanovich Parovik |
| collection | DOAJ |
| description | The paper considers hereditarity oscillator which is characterized by oscillation equation with derivatives of fractional order $\beta$ and $\gamma$, which are defined in terms of Gerasimova-Caputo. Using Laplace transform were obtained analytical solutions and the Greens function, which are determined through special functions of Mittag-Leffler and Wright generalized function. It is proved that for fixed values of $\beta = 2$ and $\gamma = 1$, the solution found becomes the classical solution for a harmonic oscillator. According to the obtained solutions were built calculated curves and the phase trajectories hereditarity oscillatory process. It was found that in the case of an external periodic influence on hereditarity oscillator may occur effects inherent in classical nonlinear oscillators. |
| first_indexed | 2024-12-12T20:51:02Z |
| format | Article |
| id | doaj.art-3990969135da4c3eab3530203f6b7a91 |
| institution | Directory Open Access Journal |
| issn | 2076-7633 2077-6853 |
| language | Russian |
| last_indexed | 2024-12-12T20:51:02Z |
| publishDate | 2015-10-01 |
| publisher | Institute of Computer Science |
| record_format | Article |
| series | Компьютерные исследования и моделирование |
| spelling | doaj.art-3990969135da4c3eab3530203f6b7a912022-12-22T00:12:25ZrusInstitute of Computer ScienceКомпьютерные исследования и моделирование2076-76332077-68532015-10-01751001102110.20537/2076-7633-2015-7-5-1001-10212367Mathematical modeling of oscillator hereditarityRoman Ivanovich ParovikThe paper considers hereditarity oscillator which is characterized by oscillation equation with derivatives of fractional order $\beta$ and $\gamma$, which are defined in terms of Gerasimova-Caputo. Using Laplace transform were obtained analytical solutions and the Greens function, which are determined through special functions of Mittag-Leffler and Wright generalized function. It is proved that for fixed values of $\beta = 2$ and $\gamma = 1$, the solution found becomes the classical solution for a harmonic oscillator. According to the obtained solutions were built calculated curves and the phase trajectories hereditarity oscillatory process. It was found that in the case of an external periodic influence on hereditarity oscillator may occur effects inherent in classical nonlinear oscillators.http://crm.ics.org.ru/uploads/crmissues/crm_2015_5/15.07.03.pdfhereditarityfractal oscillatorgeneralized function Wrightphase trajectoriesresonance |
| spellingShingle | Roman Ivanovich Parovik Mathematical modeling of oscillator hereditarity Компьютерные исследования и моделирование hereditarity fractal oscillator generalized function Wright phase trajectories resonance |
| title | Mathematical modeling of oscillator hereditarity |
| title_full | Mathematical modeling of oscillator hereditarity |
| title_fullStr | Mathematical modeling of oscillator hereditarity |
| title_full_unstemmed | Mathematical modeling of oscillator hereditarity |
| title_short | Mathematical modeling of oscillator hereditarity |
| title_sort | mathematical modeling of oscillator hereditarity |
| topic | hereditarity fractal oscillator generalized function Wright phase trajectories resonance |
| url | http://crm.ics.org.ru/uploads/crmissues/crm_2015_5/15.07.03.pdf |
| work_keys_str_mv | AT romanivanovichparovik mathematicalmodelingofoscillatorhereditarity |