Fractional Cauchy problems on bounded domains
Meerschaert, Mark M. ; Nane, Erkan ; Vellaisamy, P.
Ann. Probab., Tome 37 (2009) no. 1, p. 979-1007 / Harvested from Project Euclid
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Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain D⊂ℝd with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional time derivative. Dirichlet problems corresponding to iterated Brownian motion in a bounded domain are then solved by establishing a correspondence with the case of a half-derivative in time.
Publié le : 2009-05-15
Classification:  Fractional diffusion,  Cauchy problem,  iterated Brownian motion,  Brownian subordinator,  Caputo derivative,  uniformly elliptic operator,  bounded domain,  boundary value problem,  60G99,  35C10 
@article{1245434026,
     author = {Meerschaert, Mark M. and Nane, Erkan and Vellaisamy, P.},
     title = {Fractional Cauchy problems on bounded domains},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 979-1007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245434026}
}

Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P. Fractional Cauchy problems on bounded domains. Ann. Probab., Tome 37 (2009) no. 1, pp.  979-1007. http://gdmltest.u-ga.fr/item/1245434026/