Abstract
This paper studies the linear stochastic partial differential equation of fractional orders both in time and space variables , where
is a general Gaussian noise and
,
. The existence and uniqueness of the solution, the moment bounds of the solution are obtained by using the fundamental solutions of the corresponding deterministic counterpart represented by the Fox H-functions. Along the way, we obtain some new properties of the fundamental solutions.
Acknowledgements
Le Chen thanks Francesco Mainardi for some useful discussion and thanks Anatoly N. Kochubei for pointing out Pskhu’s paper [31].
Notes
No potential conflict of interest was reported by the authors.
Dedicated to Prof. Bernt Øksendal on the occasion of his 70th birthday.