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Integral Equations and Operator Theory

, Volume 67, Issue 1, pp 33–49 | Cite as

Existence Results for Fractional Order Semilinear Integro-Differential Evolution Equations with Infinite Delay

  • Yong Ren
  • Yan QinEmail author
  • R. Sakthivel
Article

Abstract

This paper is concerned with existence results of mild solutions for fractional order semilinear integro-differential evolution equations (FSIDEEs) and semilinear neutral integro-differential evolution equations (FSNIDEEs in short) with infinite delay in α-norm. Our tools include the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and the Krasnoselskii–Schaefer type fixed point theorem.

Mathematics Subject Classification (2000)

Primary 34A12 Secondary 34G10 

Keywords

Fractional order differential equation fractional derivative fractional integral fixed point theorem mild solution 

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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.School of MathematicsUniversity of TasmaniaHobartAustralia
  2. 2.Department of MathematicsEast China University of Science and TechnologyShanghaiChina
  3. 3.Department of MathematicsSungkyunkwan UniversitySuwonSouth Korea

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