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January  2007, 3(1): 119-128. doi: 10.3934/jimo.2007.3.119

General integro-differential equations and optimal controls on Banach spaces

Sebti Kerbal 1, and  Yang Jiang 2,

1. 

Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khoud 123, Muscat, Oman
2. 

Science College, Guizhou University, Guiyang Guizhou, P. R., China

Received  November 2005 Revised  August 2006 Published  January 2007

In this paper a general integro-differential equations on Banach space are considered. Existence of $\alpha $-mild solutions is proved. Existence of optimal controls of systems governed by general integro-differential equations is also presented.
Keywords: existence., fractional power space, Semigroup, optimal control, compactness, mild solution.
Mathematics Subject Classification: Primary: 49J22; Secondary: 47D06,34G10, 47B0.
Citation: Sebti Kerbal, Yang Jiang. General integro-differential equations and optimal controls on Banach spaces. Journal of Industrial and Management Optimization, 2007, 3 (1) : 119-128. doi: 10.3934/jimo.2007.3.119
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