Remarks on a fractional-time stochastic equation

Abstract

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 {\it tunes off the fractional} in the fractional time derivative, the solution behaves more and more like its {\it usual} counterpart.