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Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays

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Abstract

In this paper, we establish the existence and uniqueness of mild solutions for a class of semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays in α-norm. And the main tool is the fixed point theorem due to Sadovskii. Some known results are generalized.

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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, WuHu, 241000, China

    Lanying Hu

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

    Yong Ren

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

    R. Sakthivel

Authors
  1. Lanying Hu
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  2. Yong Ren
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  3. R. Sakthivel
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Corresponding author

Correspondence to Yong Ren.

Additional information

Communicated by Jerome A. Goldstein.

The second author would like to thank the Australian Research Council for funding this project through Discovery Project DP0770388.

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Hu, L., Ren, Y. & Sakthivel, R. Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays. Semigroup Forum 79, 507–514 (2009). https://doi.org/10.1007/s00233-009-9164-y

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  • DOI: https://doi.org/10.1007/s00233-009-9164-y

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