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Existence results for the fractional differential equations with multi-strip integral boundary conditions

  • Bin Di
  • Huihui PangEmail author
Original Research
  • 219 Downloads

Abstract

In this paper, we consider the existence of solutions for the fractional differential equations with multi-point and multi-strip boundary conditions. The existence results are obtained by applying Leray–Schauder’s alternative, while the uniqueness of solution is established via Banach’s contraction principle. We also consider the existence of positive solutions for the fractional differential equations with degenerated multi-strip integral boundary conditions. We come to the results by applying the Krasnoselskii’s fixed point theorem. Some examples are also presented to illustrate the main results.

Keywords

Multi-strip integral boundary conditions Fractional differential equations Green’s function Leray–Schauder’s alternative Fixed point theorems 

Mathematics Subject Classification

34B10 34B15 

Notes

Acknowledgements

The work is supported by Chinese Universities Scientific Fund (Project No. 2017LX003). The authors would like to thank the anonymous referees very much for helpful comments and suggestions which lead to the improvement of presentation and quality of the work.

Compliance with ethical standards

Conflict of interests

The authors declare that they have no competing interests.

Authors’ contributions

All authors contributed equally to the manuscript, read and approved the final draft.

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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.College of ScienceChina Agricultural UniversityBeijingPeople’s Republic of China

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