  Consider the following class of conformable time-fractional stochastic
equation $$T_{\alpha,t}^a
u(x,t)=\lambda\sigma(u(x,t))\dot{W}_t,\,\,\,\,x\in\mathbb{R},\,t\in[a,\infty),
\,\,0<\alpha<1,$$ with a non-random initial condition
$u(x,0)=u_0(x),\,x\in\mathbb{R}$ assumed to be non-negative and bounded,
$T_{\alpha,t}^a$ is a conformable time - fractional derivative,
$\sigma:\mathbb{R}\rightarrow\mathbb{R}$ is globally Lipschitz continuous,
$\dot{W}_t$ a generalized derivative of Wiener process and $\lambda>0$ is the
noise level. Given some precise and suitable conditions on the non-random
initial function, we study the asymptotic behaviour of the solution with
respect to the time parameter $t$ and the noise level parameter $\lambda$. We
also show that when the non-linear term $\sigma$ grows faster than linear, the
energy of the solution blows-up at finite time for all $\alpha\in (0,1)$.
