Copyright © 2010 Y. Peng. This is an open access article distributed under the
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A class of second-order nonlinear impulsive integro-differential equations of mixed type whose
principal part is given by time-varying generating operators in fractional power spaces is considered. We introduce the reasonable PC--mild solution of second-order nonlinear impulsive integro-differential equations of mixed type and prove its existence. The existence of optimal controls for a Lagrange problem of systems governed by second-order nonlinear impulsive integro-equations of mixed type is also presented. An example is given for demonstration.