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Study a class of nonlinear fractional non-autonomous evolution equations with delay

  • Haide Gou
  • Baolin LiEmail author
Article
  • 124 Downloads

Abstract

In this paper, we deal with a class of nonlinear fractional non-autonomous evolution equations with delay by using Hilfer fractional derivative, which generalized the famous Riemann–Liouville fractional derivative. Combining techniques of fractional calculus, measure of noncompactness and some fixed point theorem, we obtain new existence result of mild solutions when the associated semigroup is not compact. Furthermore, the assumptions that the nonlinear term satisfies some growth condition and noncompactness measure condition. The results obtained improve and extend some related conclusions. Finally, two examples will be presented to illustrate the main results.

Keywords

Non-autonomous evolution equations Mild solutions Hilfer fractional derivative 

Mathematics Subject Classification

34K30 34K45 35B10 47D06 

Notes

Acknowledgements

We wish to thank the referees for their valuable comments.

Author Contributions

All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

Compliance with ethical standards

Conflict of interest

All the authors declare that they have no competing interests.

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© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsNorthwest Normal UniversityLanzhouPeople’s Republic of China

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