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We study the spectral heat content for a class of open sets with fractalboundaries determined by similitudes in $\mathbb{R}^{d}$, $d\geq 1$, withrespect to subordinate killed Brownian motions via $\alpha/2$-stablesubordinators and establish the asymptotic behavior of the spectral heatcontent as $t\to 0$ for the full range of $\alpha\in (0,2)$. Our main theoremsshow that these asymptotic behaviors depend on whether the sequence oflogarithms of the coefficients of the similitudes is arithmetic when $\alpha\in[d-\b,2)$, where $\b$ is the interior Minkowski dimension of the boundary ofthe open set. The main tools for proving the theorems are the previous resultson the spectral heat content for Brownian motions and the renewal theorem.

Spectral heat content on a class of fractal sets for subordinate killed Brownian motions