Exact null controllability for fractional nonlocal integrodifferential equations via implicit evolution system.

*(English)*Zbl 1251.93029Summary: We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract results, two examples are provided.

##### MSC:

93B05 | Controllability |

34A08 | Fractional ordinary differential equations |

45J05 | Integro-ordinary differential equations |

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\textit{A. Debbouche} and \textit{D. Baleanu}, J. Appl. Math. 2012, Article ID 931975, 17 p. (2012; Zbl 1251.93029)

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