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Topological structure of the solution set for fractional non-instantaneous impulsive evolution inclusions

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Abstract

In this paper, we study the topological structure of the solution set for fractional non-instantaneous impulsive evolution inclusions on a compact interval. We show that the solution set for our problem is nonempty, compact and moreover a \(R_{\delta }\)-set.

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Acknowledgements

The authors thank the referees for carefully reading the manuscript and for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, People’s Republic of China

    JinRong Wang

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, People’s Republic of China

    JinRong Wang

  3. Department of Mathematics, Faculty of Science, King Faisal University, Al-Ahasa, 31982, Saudi Arabia

    A. G. Ibrahim

  4. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    D. O’Regan

Authors
  1. JinRong Wang
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  2. A. G. Ibrahim
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  3. D. O’Regan
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Corresponding author

Correspondence to JinRong Wang.

Additional information

The authors acknowledge the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Unite Foundation of Guizhou Province ([2015]7640), Graduate ZDKC ([2015]003), and Deanship of Scientific Research of King Faisal University of Saudi Arabia (No. 170060).

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Wang, J., Ibrahim, A.G. & O’Regan, D. Topological structure of the solution set for fractional non-instantaneous impulsive evolution inclusions. J. Fixed Point Theory Appl. 20, 59 (2018). https://doi.org/10.1007/s11784-018-0534-5

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  • DOI: https://doi.org/10.1007/s11784-018-0534-5

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