  Motivated by the extensive investigations of integro-differential equations
on $\mathbb{R}^n$, we consider nonlocal filtration type equations with rough
kernels on the Heisenberg group $\mathbb{H}^n$. We prove the existence and
uniqueness of weak solutions corresponding to suitable initial data.
Furthermore, we obtain the large time behavior of solutions and the uniform
H\"older regularity of sign-changing solutions for the porous medium type
equations ($m\geq 1$). Notice that both conformal fractional operators
$\mathscr{L}_{\alpha/2}$ and pure power fractional operators
$\mathscr{L}^{\alpha/2}$ on the Heisenberg group $\mathbb{H}^n$ have their
integral representations with suitable kernels. Therefore, all the results in
this paper will hold for these equations with operators
$\mathscr{L}_{\alpha/2}$ or $\mathscr{L}^{\alpha/2}$.
