Space-time fractional stochastic equations on regular bounded open domains
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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.
Acknowledgements
This work has been supported in part by projects MTM2012-32674 and MTM2015--71839--P (co-funded with Feder funds), of the DGI, MINECO, Spain. N. Leonenko was supported in particular by Cardiff Incoming Visiting Fellowship Scheme and International Collaboration Seedcorn Fund and Australian Research Council’s Discovery Projects funding scheme (project number DP160101366).
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Articles in the same Issue
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Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 19–5–2016)
- Round Table Discussion
- Fractional Calculus: D’où venons-nous? Que sommes-nous? Où allons-nous?
- Survey Paper
- Models of dielectric relaxation based on completely monotone functions
- Survey Paper
- Space-time fractional stochastic equations on regular bounded open domains
- Discussion Paper
- Geometric interpretation of fractional-order derivative
- Survey Paper
- Fractional calculus in image processing: a review
- Research Paper
- Structural derivative based on inverse Mittag-Leffler function for modeling ultraslow diffusion
- Research Paper
- On the regional controllability of the sub-diffusion process with Caputo fractional derivative
- Discussion Survey
- There’s plenty of fractional at the bottom, I: Brownian motors and swimming microrobots
- Research Paper
- On a fractional differential inclusion with “maxima”
- Research Paper
- On time-fractional representation of an open system response
- Archive Paper
- On the summation of Taylor’s series on the contour of the domain of summability