Generalized time-fractional kinetic-type equations with multiple parameters

2024/10/14 by Luca Angelani, Alessandro De Gregorio, Angelani, Luca +3
Mathematics · #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2410.10608

openalex publication_date 2024/10/14 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28

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.

Related

• Fractional Diffusion-Telegraph Equations and their Associated Stochastic Solutions
• On the solutions of certain fractional kinetic equations involving E^γ,q_k,α,β(.)
• Generalized Fractional Kinetic Equations Involving the generalized modified k-Bessel function
• Generalized space-time fractional stochastic kinetic equation
• Certain Fractional Kinetic Equations Involving Generalized k-Bessel Function