LAUSR

In this paper we consider a class of fractional nonlinear neutral stochastic evolution inclusions with nonlocal initial conditions in Hilbert space. Using fractional calculus, stochastic analysis theory, operator semigroups and Bohnenblust–Karlin’s fixed point theorem, a new set of sufficient conditions are formulated and proved for the existence of solutions and the approximate controllability of fractional nonlinear stochastic differential inclusions under the assumption that the associated linear part of the system is approximately controllable. An example is provided to illustrate the theory.