Periodic solutions of fractional differential equations with delay

Abstract

In this paper, we give a necessary and sufficient conditions for the existence and uniqueness of periodic solutions of inhomogeneous abstract fractional differential equations with delay. The conditions are obtained in terms of R-boundedness of operator-valued Fourier multipliers determined by the abstract model.

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Correspondence to Carlos Lizama.

Additional information

The first author is partially supported by FONDECYT Grant 1100485.

The second author is partially financed by FONDECYT de Iniciación 11075046.

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Lizama, C., Poblete, V. Periodic solutions of fractional differential equations with delay. J. Evol. Equ. 11, 57–70 (2011). https://doi.org/10.1007/s00028-010-0081-z

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Mathematics Subject Classification (2000)

  • 34G10
  • 34K13
  • 47D06

Keywords

  • Operator-valued Fourier multipliers
  • R-boundedness
  • Periodic vector-valued Lebesgue spaces
  • Delay equations