Generalized time-fractional kinetic-type equations with multiple parameters

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Angelani, Luca, De Gregorio, Alessandro, Garra, Roberto
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913545138995200
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
id 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