Scaling transformation of nonzero initial condition

Question

I'm trying to find the self similar solution of the fractional heat equation ,$\frac{\partial^{\alpha} u}{\partial t^{\alpha}} = \frac{\partial^{2} u}{\partial x^{2}}+ k, 0<\alpha <1, t>0,$ with initial condition $u(x,0)=f(x)$. I'm using the following scaling transformation $t =\lambda \bar{t}, x = \lambda^{p} \bar{x}, u =\lambda^{q} \bar{u}$. Now i'm struggling to find the transformed initial condition. Can any one guide me to get through this problem?