Nonlocal diffusion equations in Carnot groups

Let G be a Carnot group. We study nonlocal diffusion equations in domain $$\Omega$$ of the form $$\begin{aligned} u_t^\epsilon (x,t)=\int _{G}\frac{1}{\epsilon ^2}K_{\epsilon }(x,y)(u^\epsilon (y,t)-u^\epsilon (x,t))\,dy, \qquad x\in \Omega \end{aligned}$$ with $$u^\epsilon =g(x,t)$$ for $$x\notin \Omega$$ . For an appropriated rescaled kernel $$K_\epsilon$$ , we apply Taylor series development groups order to prove that solutions $$u^\epsilon$$ uniformly approximate solution certain local Dirichlet problem when $$\epsilon \rightarrow 0$$