State space representation for fractional order transfer function

Question

What is the state space representation for the following filters?

• $H(s)=\frac{Y(s)}{U(s)}=\frac1{s^\frac12}$
• $H(s)=\frac{Y(s)}{U(s)}=\frac1{s^\frac12+1}$

Where $u(t)$ is the input and $y(t)$ is the output. The transfer function orders are fractional. I look for $A$, $B$, $C$, $D$.

$$\dot X=AX+BU\\Y=CX+DU$$