substitution of $u_\mu(t,x)=\text{constant}\times u(\mu^\alpha t,\mu x)$ in the fractional GHE shows that this is a solution if $c=\mu^{\frac{d-\gamma+\alpha}{2(p-1)}}$, so the scale invariance relation is $$u_\mu(t,x)=\mu^{\frac{d-\gamma+\alpha}{2(p-1)}}u(\mu^\alpha t,\mu x).$$

substitution of $u_\mu(t,x)=\text{constant}\times u(\mu^\alpha t,\mu x)$ in the fractional GHE shows that this is a solution if $\text{constant}=\mu^{\frac{d-\gamma+\alpha}{2(p-1)}}$, so the scale invariance relation is $$u_\mu(t,x)=\mu^{\frac{d-\gamma+\alpha}{2(p-1)}}u(\mu^\alpha t,\mu x).$$