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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.

Approximate controllability results for fractional semilinear integro-differential inclusions in Hilbert spaces