  We study stochastic heat equations in the sense of Walsh defined by fractal
Laplacians on Cantor-like sets. For this purpose, we first investigate the
corresponding heat kernels. Then, we prove existence and uniqueness of mild
solutions to stochastic heat equations provided some Lipschitz and linear
growth conditions. We establish H\"older continuity in space and time and
compute the H\"older exponents. Moreover, we address the question of weak
intermittency.
