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arXiv · 2410.10608

Generalized time-fractional kinetic-type equations with multiple parameters

Luca Angelani·Alessandro De Gregorio·Roberto Garra
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Abstract

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.

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Luca Angelani, Alessandro De Gregorio, Roberto Garra. 2024-10-14. Generalized time-fractional kinetic-type equations with multiple parameters. https://arxiv.org/abs/2410.10608

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