Anomalous random flights and time-fractional run-and-tumble equations
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913546379460608 |
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| author | Angelani, Luca De Gregorio, Alessandro Garra, Roberto Iafrate, Francesco |
| author_facet | Angelani, Luca De Gregorio, Alessandro Garra, Roberto Iafrate, Francesco |
| contents | Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provides a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anomalous random flights and time-fractional run-and-tumble equations Angelani, Luca De Gregorio, Alessandro Garra, Roberto Iafrate, Francesco Statistical Mechanics Mathematical Physics Probability Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provides a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions. |
| title | Anomalous random flights and time-fractional run-and-tumble equations |
| topic | Statistical Mechanics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2404.15941 |