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On the approximate controllability of semilinear fractional differential systems. (English) Zbl 1228.34093
Summary: Fractional differential equations have wide applications in science and engineering. We consider a class of control systems governed by the semilinear fractional differential equations in Hilbert spaces. By using the semigroup theory, the fractional power theory and fixed point strategy, a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems. The results are established under the assumption that the associated linear system is approximately controllable. Further, we extend the result to study the approximate controllability of fractional systems with nonlocal conditions. An example is provided to illustrate the application of the obtained theory.

##### MSC:
 34H05 Control problems involving ordinary differential equations 34A08 Fractional ordinary differential equations 47H10 Fixed-point theorems
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