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We introduce a nonlocal control condition and the notion of approximatecontrollability for fractional order quasilinear control inclusions.Approximate controllability of a fractional control nonlocal delay quasilinearfunctional differential inclusion in a Hilbert space is studied. The resultsare obtained by using the fractional power of operators, multi-valued analysis,and Sadovskii's fixed point theorem. Main result gives an appropriate set ofsufficient conditions for the considered system to be approximatelycontrollable. As an example, a fractional partial nonlocal control functionaldifferential inclusion is considered.

Approximate Controllability of Fractional Delay Dynamic Inclusions with Nonlocal Control Conditions