Large-time and small-time behaviors of the spectral heat content for time-changed stable processes

We study the large-time and small-time asymptotic behaviors of spectral heat content for time-changed stable processes, where time change belongs to a large class inverse subordinators. For behavior, decays polynomially with decay rate determined by Laplace exponent underlying subordinator, which is in sharp contrast exponential observed case when subordinator. On other hand, behavior exhibits three different regimes, both index process.