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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 4, Pages 692–718
DOI: https://doi.org/10.4213/tvp5150 (Mi tvp5150) 		 
This article is cited in 40 scientific papers (total in 40 papers)

Fractional diffusion–telegraph equations and their associated stochastic solutions

M. D'Ovidioa, F. Politob

a 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
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DOI: https://doi.org/10.4213/tvp5150
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
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 4, Pages 552–574
DOI: https://doi.org/10.1137/S0040585X97T988812
Bibliographic databases:
Document Type: Article
Language: English
Citation: M. D'Ovidio, F. Polito, “Fractional diffusion–telegraph equations and their associated stochastic solutions”, Teor. Veroyatnost. i Primenen., 62:4 (2017), 692–718; Theory Probab. Appl., 62:4 (2018), 552–574
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v62/i4/p692
    • This publication is cited in the following 40 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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