We study here a generalization of the time-fractional relativistic diffusion equation based on the application of Caputo fractional derivatives of a function with respect to another function. We find the Fourier transform of the fundamental solution and discuss the probabilistic meaning of the results obtained in relation to the time-scaled fractional relativistic stable process. We briefly consider also the application of fractional derivatives of a function with respect to another function in order to generalize fractional Riesz-Bessel equations, suggesting their stochastic meaning.

A Note on the Generalized Relativistic Diffusion Equation / Beghin, Luisa; Garra, Roberto. - In: MATHEMATICS. - ISSN 2227-7390. - 7:(2019), pp. 1-9.

A Note on the Generalized Relativistic Diffusion Equation

Luisa Beghin;Roberto Garra
2019

Abstract

We study here a generalization of the time-fractional relativistic diffusion equation based on the application of Caputo fractional derivatives of a function with respect to another function. We find the Fourier transform of the fundamental solution and discuss the probabilistic meaning of the results obtained in relation to the time-scaled fractional relativistic stable process. We briefly consider also the application of fractional derivatives of a function with respect to another function in order to generalize fractional Riesz-Bessel equations, suggesting their stochastic meaning.
2019
relativistic diffusion equation; Caputo fractional derivatives of a function with respect to another function; Bessel-Riesz motion
01 Pubblicazione su rivista::01a Articolo in rivista
A Note on the Generalized Relativistic Diffusion Equation / Beghin, Luisa; Garra, Roberto. - In: MATHEMATICS. - ISSN 2227-7390. - 7:(2019), pp. 1-9.
File allegati a questo prodotto
File Dimensione Formato  
Beghin_generalized-relativistic-diffusion_2019.pdf

accesso aperto

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 256.96 kB
Formato Adobe PDF
256.96 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1334272
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact