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

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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.

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Authors and Affiliations

  1. School of Mathematics, University of Tasmania, GPO Box 252C-37, Hobart, TAS, 7001, Australia

    Yong Ren

  2. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Yan Qin

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, South Korea

    R. Sakthivel

Authors
  1. Yong Ren
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  2. Yan Qin
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  3. R. Sakthivel
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Correspondence to Yan Qin.

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Ren, Y., Qin, Y. & Sakthivel, R. Existence Results for Fractional Order Semilinear Integro-Differential Evolution Equations with Infinite Delay. Integr. Equ. Oper. Theory 67, 33–49 (2010). https://doi.org/10.1007/s00020-010-1767-x

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  • DOI: https://doi.org/10.1007/s00020-010-1767-x

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