On the solution process for a stochastic fractional partial differential equation driven by space-time white noise

Let be the solution process for the following Cauchy problem for the stochastic fractional partial differential equation taking values in : where (1<[alpha]<3, [delta]<=min{[alpha]-[[alpha]],2+[[alpha]]2-[alpha]}) is the fractional differential operator with respect to the spatial variable x (see below for a definition), is an -valued space-time white noise, and u0 is an initial random datum defined on . In this paper, we study the sample path properties of the solution process. We first find the dimensions in which the process hits points, and then determine the Hausdorff and packing dimensions of the range, the graph and the level sets of the process. Our results generalize those of Mueller and Tribe (2002) and Wu and Xiao (2006) for random string processes.