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

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.