Generalized time-fractional kinetic-type equations with multiple parameters
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913545138995200 |
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| author | Angelani, Luca De Gregorio, Alessandro Garra, Roberto |
| author_facet | Angelani, Luca De Gregorio, Alessandro Garra, Roberto |
| contents | In this paper we study a new generalization of the kinetic equation emerging in run-and-tumble models. We show that this generalization leads to a wide class of generalized fractional kinetic (GFK) and telegraph-type equations depending by two (or three) parameters. We provide an explicit expression of the solution in the Laplace domain and show that, for a particular choice of the parameters, the fundamental solution of the GFK equation can be interpreted as the probability density function of a stochastic process obtained by a suitable transformation of the inverse of a subordinator. Then, we discuss some particular interesting cases, such as generalized telegraph models, diffusion fractional equations involving higher order time derivatives and fractional integral equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10608 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized time-fractional kinetic-type equations with multiple parameters Angelani, Luca De Gregorio, Alessandro Garra, Roberto Statistical Mechanics Mathematical Physics In this paper we study a new generalization of the kinetic equation emerging in run-and-tumble models. We show that this generalization leads to a wide class of generalized fractional kinetic (GFK) and telegraph-type equations depending by two (or three) parameters. We provide an explicit expression of the solution in the Laplace domain and show that, for a particular choice of the parameters, the fundamental solution of the GFK equation can be interpreted as the probability density function of a stochastic process obtained by a suitable transformation of the inverse of a subordinator. Then, we discuss some particular interesting cases, such as generalized telegraph models, diffusion fractional equations involving higher order time derivatives and fractional integral equations. |
| title | Generalized time-fractional kinetic-type equations with multiple parameters |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2410.10608 |