In this paper, we prove the maximal regularity property of an abstract fractional differential equation with finite delay on periodic Besov and Triebel–Lizorkin spaces and use these results to guarantee the existence and uniqueness of periodic solution of a neutral fractional differential equation with finite delay. The main tool used to achieve our goal is an operator-valued version of Miklhin’s Fourier multiplier theorem and fixed-point argument.
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The authors are partially financed by FONDECYT 1110090. The second author is financed by MECESUP PUC 0711.
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Poblete, V., Pozo, J.C. Periodic solutions of a fractional neutral equation with finite delay. J. Evol. Equ. 14, 417–444 (2014). https://doi.org/10.1007/s00028-014-0221-y
Mathematics Subject Classification (2010)
- Maximal regularity
- Fourier multipliers
- Strong solutions
- Fractional neutral equations