Some stochastic time-fractional diffusion equations with variable coefficients and time dependent noise

Guannan Hu

Some stochastic time-fractional diffusion equations with variable coefficients and time dependent noise

Probability 2016-05-09 v1

Authors: Guannan Hu

Abstract

We prove the existence and uniqueness of mild solution for the stochastic partial differential equation $\left(\partial^\alpha - \textit{B} \right) u(t,x)= u(t,x) \cdot \dot{W}(t,x),$ where $\alpha \in (1/2, 1)\cup(1, 2);$ $\textit{B}$ is an uniform elliptic operator with variable coefficients and $\dot W$ is a Gaussian noise general in time with space covariance given by fractional, Riesz and Bessel kernel.

Keywords

stochastic partial differential equations fractional diffusion equations stochastic differential equations

Cite

@article{arxiv.1605.01831,
  title  = {Some stochastic time-fractional diffusion equations with variable coefficients and time dependent noise},
  author = {Guannan Hu},
  journal= {arXiv preprint arXiv:1605.01831},
  year   = {2016}
}

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