Approximate Controllability of Fractional Neutral Stochastic Functional Integro-Differential Inclusions with Infinite Delay

In this paper, we investigate the approximate controllability for a class of fractional neutral stochastic functional integro-differential inclusions involving the Caputo derivative in Hilbert spaces. A new set of sufficient conditions are formulated and proved for the approximate controllability of fractional stochastic integro-differential inclusions under the assumption that the associated linear part of system is approximately controllable. The main techniques rely on the fractional calculus, operator semigroups and Bohnenblust–Karlin’s fixed point theorem. An example is given to illustrate the obtained theory.