Approximate Controllability of Semi-Linear Neutral Integro-Differential Equations with Nonlocal Conditions

  • Hai Huang
  • Xianlong FuEmail author


In this work, by theory of analytic semi-groups, fractional powers of operators, and resolvent operator theory, we study the approximate controllability of a semi-linear neutral integro-differential equation with nonlocal conditions. Under the assumption of controllability on the corresponding linear system, we obtain the sufficient conditions for the considered semi-linear integro-differential system. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal condition appearing in literature is not required here. An example is also provided to illustrate the application of the obtained results.


Neutral integro-differential equation Approximate controllability Resolvent operator Fractional power operator Nonlocal condition 



We would like to thank the referees greatly for the valuable comments and suggestions to this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghaiPeople’s Republic of China

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