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Periodic Solutions and -Asymptotically Periodic Solutions to Fractional Evolution Equations

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  • Jia Mu
  • Yong Zhou
  • Li Peng

Abstract

This paper deals with the existence and uniqueness of periodic solutions, -asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.

Suggested Citation

  • Jia Mu & Yong Zhou & Li Peng, 2017. "Periodic Solutions and -Asymptotically Periodic Solutions to Fractional Evolution Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-12, April.
    • Handle: RePEc:hin:jnddns:1364532
    DOI: 10.1155/2017/1364532
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    References listed on IDEAS

    as
    1. Alvarez-Pardo, Edgardo & Lizama, Carlos, 2015. "Weighted pseudo almost automorphic mild solutions for two-term fractional order differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 154-167.
    2. Shu, Xiao-Bao & Xu, Fei & Shi, Yajing, 2015. "S-asymptotically ω-positive periodic solutions for a class of neutral fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 768-776.
    3. I. Area & J. Losada & J. J. Nieto, 2014. "On Fractional Derivatives and Primitives of Periodic Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, August.
    4. Jia Mu & Hongxia Fan, 2012. "Positive Mild Solutions of Periodic Boundary Value Problems for Fractional Evolution Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, April.
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