A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1<r<2

In this manuscript, we mainly focus on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1<r<2. The primary outcomes of our manuscript are proved by using the results and facts associated with fractional calculus, multivalued maps, and Bohnenblust and Karlin's fixed point theorem. Firstly, we focus the approximate controllability and then we extend the discussion to the system with nonlocal conditions. Lastly, we provide an application for the illustration of the obtained theoretical results.