This article is cited in 41 papers

Fractional diffusion–telegraph equations and their associated stochastic solutions

M. D'Ovidio^a, F. Polito<sup>b

a</sup> Dipartimento di Scienze di Base e Applicate per l'Ingegneria, «Sapienza» Università di Roma, Roma
^b Dipartimento di Matematica «G. Peano», Università degli Studi di Torino, Torino, Italy

Abstract: We present the stochastic solution to a generalized fractional partial differential equation (fPDE) involving a regularized operator related to the so-called Prabhakar operator and admitting as specific cases, among others, 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 stochastic differential equation (SDE) is derived and discussed.

Keywords: time-changed processes, Lévy processes, Prabhakar operators, regularized Prabhakar derivative, fractional derivatives, stochastic solution.

Received: 23.03.2015
Revised: 10.04.2017
Accepted: 10.04.2017

Language: English

DOI: 10.4213/tvp5150

 English version: Theory of Probability and its Applications, 2018, 62:4, 552–574

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