Abstract and Applied Analysis
Volume 2010 (2010), Article ID 213503, 16 pages
doi:10.1155/2010/213503
Research Article

Second-Order Nonlinear Impulsive Integro-Differential Equations of Mixed Type and Optimal Controls in Fractional Power Spaces

Y. Peng

Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China

Received 23 September 2010; Revised 20 November 2010; Accepted 27 November 2010

Academic Editor: Irena Lasiecka

Copyright © 2010 Y. Peng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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- 𝛼 -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.