Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function

Abstract

In this paper, we formulate a new set of sufficient conditions for the approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay in Hilbert space. Bohnenblust–Karlin’s fixed point theorem, Mainardi’s function, fractional calculus and operator semigroups are used to establish the results under the assumption that the corresponding linear system is approximately controllable. In the end, an example is provided to illustrate the applicability of the obtained theoretical results.