In this article, by using a fixed point theorem, we study the existence and regularity of mild solutions for a class of abstract neutral functional differential equations with infinite delay. The fraction power theory and alpha-norm is used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. A stability result for the autonomous case is also established. We conclude with an example that illustrates the applications of the results obtained.
Submitted September 16, 2012. Published February 21, 2013.
Math Subject Classifications: 34K25, 34K30, 34G20.
Key Words: Neutral functional differential equation; analytic semigroup; fractional power operator; linearized stability; infinite delay.
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| Xianlong Fu |
Department of Mathematics
East China Normal University
Shanghai, 200241, China
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