Approximate controllability of fractional impulsive stochastic functional differential inclusions with infinite delay and fractional sectorial operators

In this paper, the approximate controllability of fractional impulsive stochastic functional differential inclusions with infinite delay and fractional sectorial operators is considered. By using the stochastic analysis, the fractional sectorial operators and a fixed-point theorem for multi-valued maps, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the fractional impulsive stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is also given to illustrate the obtained theory.