2015/04/03 by V. V. Anh, Vo Anh, Nikolai Leonenko +6
Computer Science · Mathematics · #35F45 #35J08 #35S11 #47D03 #Advanced Mathematical Modeling in Engineering #Bessel function #Boundary value problem #Bounded function #Covariance operator #Dirichlet distribution #Dynamical Systems (math.DS) #Eigenvalues and eigenvectors #FOS: Mathematics #Fractional Differential Equations Solutions #Fractional calculus #Hilbert space #Laplace operator #Mathematical analysis #Mathematics #Nonlinear Differential Equations Analysis #Physics #Polynomial #Pure mathematics #Space (punctuation) #Type (biology) #White noise #math.DS #msc:35F45 #msc:35J08 #msc:35S11 #msc:47D03
paper · pdf · doi:10.48550/arxiv.1504.00803
openalex publication_date 2015/04/03 · arxiv created 2017/01/13 · arxiv updated 2017/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.