On the approximate boundary controllability of some partial functional integrodifferential equations with finite delay in Banach spaces

This work concerns the study of approximate boundary controllability for some nonlinear partial functional integrodifferential equations with finite delay arising in modeling materials memory, framework general Banach spaces. We give sufficient conditions that ensure system by supposing its linear undelayed part is approximately controllable, admits a resolvent operator sense Grimmer, and making use fixed-point Theorem continuity uniform norm-topology. As result, we obtain generalization several important results literature, without assuming compactness boundedness term. An example applications given illustration.