We consider the fractional stochastic heat type equation egin{align*}partial_t u_t(x)=-(-Delta)^{lpha/2}u_t(x)+xisigma(u_t(x))dot{F}(t,x), xin D, t>0, end{align*} with nonnegative bounded initial condition,where $lphain (0,2]$, $xi>0$ is the noise level,$sigma:mathbb{R}ightarrowmathbb{R}$ is a globally Lipschitz functionsatisfying some growth conditions and the noise term behave in space like theRiez kernel and is possibly correlated in time and $D$ is the open ball ofradius $R>0$, centered at the origin. When the noise term is not correlated intime, we establish a change in the growth of the solution of these equationsdepending on the noise level $xi$. On the other hand when the noise termbehaves in time like the fractional Brownian motion with index $Hin (1/2,1)$,We also derive explicit bounds leading to a well-known weakly$ho$-intermittency property.
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