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Space-time fractional stochastic equations on regular bounded open domains

Anh, V. V., Leonenko, Nikolai and Ruiz-Medina, M.D. 2016. Space-time fractional stochastic equations on regular bounded open domains. Fractional Calculus and Applied Analysis 19 (5) , pp. 1161-1199.

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Abstract

Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian spatiotemporal white noise, are considered here. Sufficient conditions for the definition of a weak-sense Gaussian solution, in the mean-square sense, are derived. The temporal, spatial and spatiotemporal Hölder continuity, in the mean-square sense, of the formulated solution is obtained, under suitable conditions, from the asymptotic properties of the Mittag-Leffler function, and the asymptotic order of the eigenvalues of a fractional polynomial of the Dirichlet negative Laplacian operator on such bounded open domains.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Caputo-Djrbashian fractional-in-time derivative; Dirichlet regular bounded open domains; eigenfunction expansion; fractional pseudodifferential elliptic operators; Gaussian spatiotemporal white noise measure; Mittag-Leffler function; Riemannan-Liouville fractional integral and derivative; stochastic boundary value problems
Publisher: Springer Verlag
ISSN: 1311-0454
Date of First Compliant Deposit: 12 July 2016
Date of Acceptance: 25 June 2016
Last Modified: 11 Oct 2017 11:24
URI: http://orca.cf.ac.uk/id/eprint/92471

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