Remarks On A Fractional-Time Stochastic Equation

We consider a class of a 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 [ALFA Lat. Am. J. Probab. Math. Stat. 12 (2015), pp. 551-571] and extented in [Stochastic Process Appl. 126 (2016), pp. 1184-1205] and [Electron. Commun. Probab. 23 (2018)]. 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.