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Asymptotically Periodic Solutions for Caputo Type Fractional Evolution Equations

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Abstract

In this paper, we prove that Caputo type linear fractional evolution equations do not have nonconstant periodic solutions. Then, we study asymptotically periodic solutions of semilinear fractional evolution equations and establish existence and uniqueness results by using theory of semigroup and fixed point theorems. Finally, two examples are given to illustrate the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, P.R. China

    Lulu Ren

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, P.R. China

    JinRong Wang

  3. Department of Mathematical Analysis and Numerical Mathematics Comenius, University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  4. Mathematical Institute, Slovak Academy of Sciences, Štefánikova, 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

Authors
  1. Lulu Ren
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  2. JinRong Wang
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  3. Michal Fečkan
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Correspondence to Lulu Ren.

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Ren, L., Wang, J. & Fečkan, M. Asymptotically Periodic Solutions for Caputo Type Fractional Evolution Equations. FCAA 21, 1294–1312 (2018). https://doi.org/10.1515/fca-2018-0068

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