Stochastic fractional heat equation with general rough noise

Bin Qian, Ran Wang

Consider the following nonlinear one-dimensional stochastic fractional heat equation $$\frac{\partial }{\partial t}u(t,x)=-(-\Delta {)}^{\alpha /2}u(t,x)+\sigma (t,x,u(t,x))\dot{W}(t,x),$$ wher…