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Semigroup Forum

, Volume 99, Issue 3, pp 591–606 | Cite as

Fractional differential equations of Sobolev type with sectorial operators

  • Yong-Kui Chang
  • Rodrigo PonceEmail author
  • Silvia Rueda
Research Article
  • 129 Downloads

Abstract

This paper treats the asymptotic behavior of resolvent operators of Sobolev type and its applications to the existence and uniqueness of mild solutions to fractional functional evolution equations of Sobolev type in Banach spaces. We first study the asymptotic decay of some resolvent operators (also called solution operators) and next, by using fixed point results, we obtain the existence and uniqueness of solutions to a class of Sobolev type fractional differential equation. We notice that, the existence or compactness of an operator \(E^{-1}\) is not necessarily needed in our results.

Keywords

Sobolev type differential equations Asymptotic decay Fractional derivative Fractional resolvent families 

Notes

Acknowledgements

The authors are grateful to the editor and anonymous referees for carefully reading this manuscript and giving valuable suggestion for improvements. Part of this work was done while S. Rueda was in the Master degree program in Mathematics at the Universidad de Talca.

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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.Instituto de Matemática y FísicaUniversidad de TalcaTalcaChile
  3. 3.Departamento de Matemática y ComputaciónUniversidad de Santiago de ChileSantiagoChile

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