Space–time fractional stochastic partial differential equations

We consider non-linear time-fractional stochastic heat type equation ∂tβut(x)=−ν(−Δ)α/2ut(x)+It1−β[σ(u)W⋅(t,x)] in (d+1)(d+1) dimensions, where ν>0,β∈(0,1)ν>0,β∈(0,1), α∈(0,2]α∈(0,2] and d