Geodesic
Fractional diffusion--telegraph equations and their associated stochastic solutions
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 692-718

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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, Prabhakar operators, regularized Prabhakar derivative, fractional derivatives, stochastic solution.
Mots-clés : Lévy processes 
@article{TVP_2017_62_4_a3,
     author = {M. D'Ovidio and F. Polito},
     title = {Fractional diffusion--telegraph equations and their associated stochastic solutions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {692--718},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a3/}
}
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M. D'Ovidio; F. Polito. Fractional diffusion--telegraph equations and their associated stochastic solutions. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 692-718. http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a3/