In this paper, we consider a class of fractional integro-differentialinclusions in Hilbert spaces. This paper deals with the approximatecontrollability for a class of fractional integro-differential control systems.First, we establishes a set of sufficient conditions for the approximatecontrollability for a class of fractional semilinear integro-differentialinclusions in Hilbert spaces. We use Bohnenblust-Karlin's fixed point theoremto prove our main results. Further, we extend the result to study theapproximate controllability concept with nonlocal conditions. An example isalso given to illustrate our main results.
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