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In this paper, we study the following nonlinear fractional stochastic partial differential equationwheredenotes the Markovian generator of a stable-like Feller process with variable order andis a measurable function. The forcing noise denoted byis a spatially inhomogeneous white noise. Under some assumptions on the catalytic measure of the inhomogeneous Brownian sheet, we study the moment bounds for the solution. As a byproduct, we prove that the solution is weakly full intermittent based on the moment estimates of the solution. We also study the Hölder regularity of the solution with respect to the temporal and spatial variables, respectively.

Solving a nonlinear fractional SPDE with spatially inhomogeneous white noise