Abstract: By using the fixed point theorem, we investigated the existence and uniqueness of mild solutions for a class of  delay stochastic evolution equations with α∈(0,1) order Riemann-Liouville fractional derivatives in Hilbert spaces, and proved the Ulam-Hyers stability of the solution. Finally, an example was given to illustrate the applicability of the obtained conclusions.

Key words: Riemann-Liouville fractional derivative, stochastic evolution equation, delay, Ulam-Hyers stability