We present the stochastic solution to a generalized fractional partial differential equation involving a regularized operator related to the so-called Prabhakar operator and admitting, amongst others, as specific cases the fractional diffusion equation and the fractional telegraph equation. The stochastic solution is expressed as a Lévy process time-changed with the inverse process to a linear combination of (possibly subordinated) independent stable subordinators of different indices. Furthermore a related SDE is derived and discussed.

Fractional Diffusion-Telegraph Equations and their Associated Stochastic Solutions

POLITO, Federico
2017-01-01

Abstract

We present the stochastic solution to a generalized fractional partial differential equation involving a regularized operator related to the so-called Prabhakar operator and admitting, amongst others, as specific cases the fractional diffusion equation and the fractional telegraph equation. The stochastic solution is expressed as a Lévy process time-changed with the inverse process to a linear combination of (possibly subordinated) independent stable subordinators of different indices. Furthermore a related SDE is derived and discussed.
2017
62
4
692
718
https://arxiv.org/pdf/1307.1696
Time-changed processes, Lévy processes, Prabhakar operator, Fractional derivatives, Stochastic solution
D'Ovidio Mirko; Polito Federico
File in questo prodotto:
File Dimensione Formato  
published.pdf

Accesso riservato

Descrizione: pdf editoriale
Tipo di file: PDF EDITORIALE
Dimensione 497.94 kB
Formato Adobe PDF
497.94 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/2318/1647248
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 30
  • ???jsp.display-item.citation.isi??? 26
social impact