Is the following equality of convolutions True?
$1*h_\alpha*\Delta u(x)=g_\alpha*\Delta u(x), \ x \in \mathbb{R}^n. $
Where $h_\alpha (t)=g'(t)$ and $g(t)=t^{\alpha-1}/\Gamma(\alpha+1)$, $t>0$ with $\alpha \in (0,1)$. The function $u:[0,\infty)\times \mathbb{R}^n \to \mathbb{R}$ is sufficiently smooth. I am trying prove replacing $\Delta u$ for a $C^\infty$ with compact suport function $\phi$, but i cant arrive anywhere. Futhermore, dont want prove to the distribution sense.