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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 4, Pages 692–718 (Mi tvp5150)  

This article is cited in 3 scientific papers (total in 3 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

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.

DOI: https://doi.org/10.4213/tvp5150

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

Bibliographic databases:

Received: 23.03.2015
Revised: 10.04.2017
Accepted:10.04.2017
Language:

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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\paper Fractional diffusion--telegraph equations and their associated stochastic solutions
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\pages 692--718
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  • http://mi.mathnet.ru/eng/tvp/v62/i4/p692

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. Colombaro, A. Giusti, S. Vitali, “Storage and dissipation of energy in Prabhakar viscoelasticity”, Mathematics, 6:2 (2018), 15, 9 pp.  crossref  isi
    2. M. D'Ovidio, P. Loreti, “Solutions of fractional logistic equations by Euler's numbers”, Phys. A, 506 (2018), 1081–1092  crossref  mathscinet  isi  scopus
    3. Derakhshan M.H., Ansari A., “Numerical Approximation to Prabhakar Fractional Sturm-Liouville Problem”, Comput. Appl. Math., 38:2 (2019)  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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