Abstract
In this paper, we investigate the approximate controllability for fractional integrodifferential inclusions of order r∈(1,2) in Banach space with sectorial operators. In particular, we obtain a new set of sufficient conditions for the approximate controllability of nonlinear fractional integrodifferential inclusions of order r∈(1,2) under the assumption that the corresponding linear system is approximately controllable. In addition, we establish the approximate controllability results for the Sobolev type fractional control system with nonlocal conditions. The results are obtained with the help of fractional derivatives, sectorial operators of type (P,η,r,γ), multivalued functions, and Bohnenblust-fixed Karlin’s point theorem. Moreover, an example is also provided to illustrate the effectiveness of the results.
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