We consider a class of fractional time stochastic equation defined on a bounded domain and show that the presence of the time derivative induces a significant change in the qualitative behaviour of the solutions. This is in sharp contrast with the phenomenon showcased in earlier works. We also show that as one tunes off the fractional in the fractional time derivative, the solution behaves more and more like its usual counterpart.
- fractional stochastic equation
- space-time white noise
- space colored noise