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Consider the following class of conformable time-fractional stochasticequation $$T_{\alpha,t}^au(x,t)=\lambda\sigma(u(x,t))\dot{W}_t,\,\,\,\,x\in\mathbb{R},\,t\in[a,\infty),\,\,0<\alpha<1,$$ 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 thenoise level. Given some precise and suitable conditions on the non-randominitial function, we study the asymptotic behaviour of the solution withrespect to the time parameter $t$ and the noise level parameter $\lambda$. Wealso show that when the non-linear term $\sigma$ grows faster than linear, theenergy of the solution blows-up at finite time for all $\alpha\in (0,1)$.

Asymptotic behavior of solution and non-existence of global solution to a class of conformable time-fractional stochastic equation