Non-Local Seismo-Dynamics: A Fractional Approach
This paper consists of a general consideration of a seismic system as a subsystem of another, larger system, exchanging with it by extensive dynamical quantities in a sequential push mode. It is shown that, unlike an isolated closed system described by the Liouville differential equation of the firs...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/9/513 |
| _version_ | 1797488183862099968 |
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| author | Vladimir Uchaikin Elena Kozhemiakina |
| author_facet | Vladimir Uchaikin Elena Kozhemiakina |
| author_sort | Vladimir Uchaikin |
| collection | DOAJ |
| description | This paper consists of a general consideration of a seismic system as a subsystem of another, larger system, exchanging with it by extensive dynamical quantities in a sequential push mode. It is shown that, unlike an isolated closed system described by the Liouville differential equation of the first order in time, it is described by a fractional differential equation of a distributed equation in the interval (0, 1] order. The key characteristic of its motion is a spectral function, representing the order distribution over the interval. As a specific case of the process, a system with single-point spectrum is investigated. It follows the fractional Poisson process method evolution, obeying via a time-fractional differential equation with a unique order. The article ends with description of statistical estimation of parameters of seismic shocks imitated by Monte Carlo simulated fractional Poisson process. |
| first_indexed | 2024-03-09T23:59:23Z |
| format | Article |
| id | doaj.art-7ff23d8722dd41b5a625d0abaf5f24c8 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T23:59:23Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-7ff23d8722dd41b5a625d0abaf5f24c82023-11-23T16:19:59ZengMDPI AGFractal and Fractional2504-31102022-09-016951310.3390/fractalfract6090513Non-Local Seismo-Dynamics: A Fractional ApproachVladimir Uchaikin0Elena Kozhemiakina1Department of Theoretical Physics, Ulyanovsk State University, Lev Tolstoy Street, 42, 432017 Ulyanovsk, RussiaDepartment of Theoretical Physics, Ulyanovsk State University, Lev Tolstoy Street, 42, 432017 Ulyanovsk, RussiaThis paper consists of a general consideration of a seismic system as a subsystem of another, larger system, exchanging with it by extensive dynamical quantities in a sequential push mode. It is shown that, unlike an isolated closed system described by the Liouville differential equation of the first order in time, it is described by a fractional differential equation of a distributed equation in the interval (0, 1] order. The key characteristic of its motion is a spectral function, representing the order distribution over the interval. As a specific case of the process, a system with single-point spectrum is investigated. It follows the fractional Poisson process method evolution, obeying via a time-fractional differential equation with a unique order. The article ends with description of statistical estimation of parameters of seismic shocks imitated by Monte Carlo simulated fractional Poisson process.https://www.mdpi.com/2504-3110/6/9/513aftershockspower lawsfractional equationsopen systemsdistributed ordersfractional Poisson process |
| spellingShingle | Vladimir Uchaikin Elena Kozhemiakina Non-Local Seismo-Dynamics: A Fractional Approach Fractal and Fractional aftershocks power laws fractional equations open systems distributed orders fractional Poisson process |
| title | Non-Local Seismo-Dynamics: A Fractional Approach |
| title_full | Non-Local Seismo-Dynamics: A Fractional Approach |
| title_fullStr | Non-Local Seismo-Dynamics: A Fractional Approach |
| title_full_unstemmed | Non-Local Seismo-Dynamics: A Fractional Approach |
| title_short | Non-Local Seismo-Dynamics: A Fractional Approach |
| title_sort | non local seismo dynamics a fractional approach |
| topic | aftershocks power laws fractional equations open systems distributed orders fractional Poisson process |
| url | https://www.mdpi.com/2504-3110/6/9/513 |
| work_keys_str_mv | AT vladimiruchaikin nonlocalseismodynamicsafractionalapproach AT elenakozhemiakina nonlocalseismodynamicsafractionalapproach |