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.
Y. Peng. "Second-Order Nonlinear Impulsive Integro-Differential Equations of Mixed Type and Optimal Controls in Fractional Power Spaces." Abstr. Appl. Anal. 2010 1 - 16, 2010. https://doi.org/10.1155/2010/213503