| Issue |
Math. Model. Nat. Phenom.
Volume 13, Number 1, 2018
Theory and applications of fractional differentiation
|
|
|---|---|---|
| Article Number | 15 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/mmnp/2018004 | |
| Published online | 26 February 2018 | |
Existence and regularity of mild solutions to fractional stochastic evolution equations
1
School of Mathematics and Statistics, Henan University,
Kaifeng
475004, P.R. China
2
Faculty of Mathematics and Computational Science, Xiangtan University,
Hunan
411105, P.R. China
3
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science King Abdulaziz University,
Jeddah
21589, Saudi Arabia
* Corresponding author: yzhou@xtu.edu.cn
Received:
22
September
2017
Accepted:
25
September
2017
This study is concerned with the stochastic fractional diffusion and diffusion-wave equations driven by multiplicative noise. We prove the existence and uniqueness of mild solutions to these equations by means of the Picard’s iteration method. With the help of the fractional calculus and stochastic analysis theory, we also establish the pathwise spatial-temporal (Sobolev-Hölder) regularity properties of mild solutions to these types of fractional SPDEs in a semigroup framework. Finally, we relate our results to the selection of appropriate numerical schemes for the solutions of these time-fractional SPDEs.
Mathematics Subject Classification: 60H15 / 35Q30 / 35K55
Key words: Fractional calculus / stochastic diffusion equations / stochastic diffusion-wave equations / mild solutions / numerical results
© EDP Sciences, 2018
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