Controllability of fractional stochastic evolution equations with nonlocal conditions and noncompact semigroups

Abstract

This article deals with the exact controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space under the assumption that the semigroup generated by the linear part is noncompact. Our main results are obtained by utilizing stochastic analysis technique, measure of noncompactness and the Mönch fixed point theorem. In the end, an example is presented to illustrate that our theorems guarantee the effectiveness of controllability results in the infinite dimensional spaces.

Keywords

• noncompact semigroups
• controllability
• stochastic evolution equations
• measure of noncompactness
• 93b05
• 60h15
• 47j35