The tempered space-fractional Cattaneo equation. (October 2022)

• Record Type: Journal Article
• Authors: Beghin, Luisa; Garra, Roberto; Mainardi, Francesco; Pagnini, Gianni
• Is Part Of: Probabilistic engineering mechanics. Volume 70(2022)
• Publication Date: 2022-10
• Subjects: Cattaneo equation -- Tempered fractional derivative -- Stochastic processes; Engineering -- Statistical methods -- Periodicals; Mechanics, Applied -- Statistical methods -- Periodicals; Probabilities -- Periodicals; Ingénierie -- Méthodes statistiques -- Périodiques; Mécanique appliquée -- Méthodes statistiques -- Périodiques; Probabilités -- Périodiques; 620.100727
• DOI: 10.1016/j.probengmech.2022.103374
• Languages: English
• ISSNs: 0266-8920

Abstract

Abstract: We consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. There is an increasing interest in the recent literature for the applications of the fractional-type Cattaneo equations to heat transfer models. Our main aim is to discuss the role played by a fractional tempered operator in this framework. We show that the fundamental solution coincides with the probability law of a time-changed Brownian motion, obtained by means of a tempered stable subordinator. We find the characteristic function of this process and we explain the main differences with previous stochastic treatments of the time-fractional Cattaneo equation. We also provide the solution of a Dirichlet problem for the tempered fractional Cattaneo equation by means of the H-Fox function.